Thank you so much Dr. Kelly for your continued love and support. Take care dear and stay blessed😃 Keep smiling😊 Enjoy every moment of your life 🌻 Have a very happy and blessed New Year!
Thank you for reminding me that I need to practice log problems until I can use logs to solve equations. I'm 78 years old, but not to old to review knowledge I neglected in my youth. The key to learning math is practicing and utilizing skills until one is proficient. The great thing about Math is that once a skill is mastered you know that knowledge is not going to change and can be used to solve more difficult problems. Math Knowledge is a Box of Tools used to solve math problems, in order to use the tools one must practice until one knows how to use the tools.
and here i am, dropped my tools box. i salute you sir for keeping your tools box maintained (i don't event know why I'm here, i just watch some smithing and stumble upon math that i hate the most)
I am also 66 yrs and maths is my favorite subject since childhood. The teacher has explained it very well which becomes so easy and interesting to follow and which was not the case with my teacher in school days. I am from Mauritius.
Excellent thank you very much. I did not think to use u-substitution. The step by step way you showed your work and reference to rules of exponents/logs was perfect.
I wrote a number of computer programs with quadratic geometry equations needing to be solved. When working out the mathematics I had to remind myself of the relationships between quotients and exponentials. Well worth going over this in detail.
As long as you are splitting up the multiplications in the logs to external addition, you might as well use Euler's Identity (e^pi*i = -1 : ln(-1) = pi*i) to tackle x = ln(1-sqrt(5)/2) / ln(3/2) = [Nodd*pi*i + ln(sqrt(5)-1) - ln(2)] / [ln(3) - ln(2)] = [ln(sqrt(5) - 1) - ln(2) / ln(3) - ln(2)] + [Nodd*pi/ln(3) - ln(2)]i, where Nodd is any odd integer. You also have x = [ln(sqrt(5) + 1) - ln(2) / ln(3) - ln(2)] + [Neven*pi/ln(3) - ln(2)]i, Neven is any even integer, and your answer is for Neven = 0.
Hello dear, in that case we may not use this substitution method. We'll have to take a different approach to handle that kind of problem. I'll try to touch the base on that kind of problem as well. Thanks for asking. You are awesome! Take care dear and stay blessed😃 Have a very happy and blessed New Year!
As soon as I saw "1 + u = u^2" I knew u = Phi, the Golden Ratio. So the most exact answer (infinite precision) is ln(Phi)/ln(3/2), or "logarithm in base three halves, of the Golden Ratio"
I'm a 68 yr. old man who was never able to pass an algebra class in college. I tried and failed three times. I've been trying to exercise my brain now that I'm retired and have been tackling algebra/math tutorials here on RUclips. I had to stop this video at the 6:40 mark...totally lost and confused! Just like when I was in school some 48 yrs ago when our class got to the using the Quadratic Formula to solve problems I was done...lost and never able to recover. Wondering if there is a teacher on this planet that can teach a person like myself who doesn't seem to possess any significant math skills. My brain fights this stuff tooth and nail.
If you have problems with math try start from the beginning and learn from there you know basic math and built your math skills up then it becomes easier to understand how to read quadric formula And other types of math it’s not easy to learn math because you have to use a lot of times to practice the brain to understand what to do step by step
Answer x= 1.18681 4^x + 6^x = 9^x 4^x/6^x + 1 = 9^x/6^x ( divide both sides by 6^x) (2/3)^x +1 = (3/2)^x introduce y= (2/3)^x, therefore 1/y= (3/2)^x hence y + 1 = 1/y y^2 + y =1 ( mutliply both sides by y) y^2 + y-1 = 0 using quadratic formulae calculator y= 0.618034 and -1.61803 Therefore (2/3)^x = 0.618034 ( I won't use -1.61803 since will log both sides, and the natural log of a negative number is undefined) x log 2/3 = log 0.618034 -0.176091 x = -0.208987 x = 0.208987/0.17091 (since both were negative numbers) x = 1.18681 Answer
So nice of you dear! You are awesome 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Take care dear and stay blessed😃
I am your regular viewer ,I have a comment ,why don't you describe or give a little literature view before solving equation and add some question for us to test ourselves?
OK, so the proof. 4x = 4 * 1.186 = 4.744. 6x = 6 * 1.186 = 7.116. therefore 4x + 6x = 11.86. Divide 11.86 by 9 and you get 1.317 not 1.186. am I missing something?
@@gibbogle The reason I was pointing this out is because it is symptomatic for both RUclipsrs and scientists. Too many scientists of today have no interest in discovering, inventing, learning or understanding anymore. They want to stand in front of a camera and perform tricks like a wizzard. They dont want people to learn or understand anything. They just want you to stand there with open mouth and say Oohhhh, Ahhhh, look at these magicians. As funny as it may seem, this is a catastrophic development.
Here I'm sitting in my holiday watching log videos...engineering jokes...study, sleep, girlfriend...pick one, you don't have time for the others🙈 good video, thank you.
So nice of you Soulemane! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Take care dear and all the best😃 Have a very happy and blessed New Year!
Can you please explain why you divided by 4x and not the other values..how do you know which value to choose or what determines which value you choose..secondly..why is u only a positive value after you solved the quadratic equation..thank you
Hello, Would you please explain me something please : You have divided by 4 ^X all the member of the equation so 4^X is the denominator but why you don't have multiply by 4^X the numerator ?? (4^X*4^X) / 4^X Sorry for this silly question. :)
A geate example of why I use Excel to solve this type of problem. I create an Excel formula with the value of X in one cell with a starting value and a modified version of the equation equaling zero in another. Then I use Excel’s solver function. Done in one minute. The only issue is sometimes you get the wrong root. Then you start with a different value of X. I get paid to get the right answer and not by how I got the right answer.
Let: (2^x )be (a), let (3^x )be( b) , then a^2 +ab -b^2=0, use casio 50FH or3650P2" fmla 01" to solve, a=0.618033988b , (reject the -1.61..),then (2^x)=0.618033988(3^x) , then x=(log0.618033988)÷(log2-log3)=1.186814393 ( exactly), just use calculator 1 step to solve x
when you divide through with 9 power x, as the first step, instead of 4 power x, it will give a perfect quadratic equation. However, the roots derived from that result in a completely different answer. x=3.880. I would love to have someone help me to understand that.
Your approach is good and does yield the correct answer of approximately 1.186. (I worked the problem as you suggested just to check the answer again.) So, I got (2/3) power x = ((-1 + sqrt(5))/2). After taking log of both sides and applying properties of logs, x = (log(-1 + sqrt(5)) - log(2)) / (log(2) - log(3)). If this was your result, too, try inputting into your calculator as I have typed out with parentheses or break down the expression into smaller and smaller pieces using approximations. Your answer may be a little different as you introduce rounding error, but you will see that you have chosen a correct method which should yield the same answer.
How can 10x = 9x? 4x + 6x = 10x, If x = 1.186 then 10 x = 11.86. 9x = 9 times 1.186 = 10.647. If I had $1000 in the bank and the bank manager told me that it was actually $900 I'd be a bit annoyed.
Can you use the associative law to rewrite the equation 9x+1x=9x then subtract 9x from each side of equation 1x=0 don't know haven't been in school or 45 yard tho maybe
@@mikenajera8834 Maybe this is true for the US math traditions... Here in Russia, if the log at the base of ten (10) is implied, we put it as "lg" (two chars), whereas "log" (three chars) is a logarithm of any valid base (except "10" and "e").
You are a tremendous help to students, PreMath! Solving by substitution is hard, and I love how you explained and showed each step!
he is one of the best teachers .
Thank you so much Dr. Kelly for your continued love and support. Take care dear and stay blessed😃 Keep smiling😊 Enjoy every moment of your life 🌻
Have a very happy and blessed New Year!
@@PreMath Thank you, sir!
I certainly agree. I come here to refresh my memory on these particular math skills since I've been teaching 8th grade math for the past two years.
@@1966lavc too good
Thank you for reminding me that I need to practice log problems until I can use logs to solve equations. I'm 78 years old, but not to old to review knowledge I neglected in my youth. The key to learning math is practicing and utilizing skills until one is proficient. The great thing about Math is that once a skill is mastered you know that knowledge is not going to change and can be used to solve more difficult problems. Math Knowledge is a Box of Tools used to solve math problems, in order to use the tools one must practice until one knows how to use the tools.
I salute you, Sir.
keep going man😊👍
and here i am, dropped my tools box. i salute you sir for keeping your tools box maintained (i don't event know why I'm here, i just watch some smithing and stumble upon math that i hate the most)
I like the way you're not afraid to rock those spelling mistakes also. That takes courage.
I am also 66 yrs and maths is my favorite subject since childhood. The teacher has explained it very well which becomes so easy and interesting to follow and which was not the case with my teacher in school days. I am from Mauritius.
If i had youtube in my school time, i would have definately passed iit. Really great platform and great job. Keep on !
Not really. Everyone would have had access to RUclips and you so would still be behind everyone just like you were at that time.
@@konjecture emotional damage!!!!
@@konjecture Logic doesn't seem to be your friend. He never said he would've been the best, he just said he would have passed.
Excellent thank you very much. I did not think to use u-substitution. The step by step way you showed your work and reference to rules of exponents/logs was perfect.
I wrote a number of computer programs with quadratic geometry equations needing to be solved. When working out the mathematics I had to remind myself of the relationships between quotients and exponentials. Well worth going over this in detail.
Just so complicated! We went from a simple 4x + 6x + 9x to rocket science!!
I had a quick look at this and could not solve easily. Thank you , I found this very relaxing to follow !
Nice bring up more these type of questions..... Well done from heart❤️
I watched this even though I had finished university 3 years ago - just to refresh my memory :-)
This method is more simple as compare to the method tell by mind your brain
Exactly.. Same
Yes
I think you mean to say mind your decision. Right?
Didn't he do the same thing?
@@mehex9858 Mind Your Brain does exist
Very beautifully done!
I just saw the video and tried solving it for an hour then i failed and saw the video till the end
You did a nice work here
yes I understand of your teaching , thank you so much specially the fraction solve equation
Nice effort for the students sir.Carey on
So nice of you Safeer!
Take care dear and stay blessed😃
good work. clear concept . up to mark. keep it up 👍
Vv nice & useful thanks
So nice of you dear
Thanks for the visit! You are awesome 👍 Take care dear and stay blessed😃 Kind regards
Very nice 👍
Thumbs up 👍👍👍
Nicely and clearly solved!
Nicely done sir!
As long as you are splitting up the multiplications in the logs to external addition, you might as well use Euler's Identity (e^pi*i = -1 : ln(-1) = pi*i) to tackle x = ln(1-sqrt(5)/2) / ln(3/2) = [Nodd*pi*i + ln(sqrt(5)-1) - ln(2)] / [ln(3) - ln(2)] = [ln(sqrt(5) - 1) - ln(2) / ln(3) - ln(2)] + [Nodd*pi/ln(3) - ln(2)]i, where Nodd is any odd integer.
You also have x = [ln(sqrt(5) + 1) - ln(2) / ln(3) - ln(2)] + [Neven*pi/ln(3) - ln(2)]i, Neven is any even integer, and your answer is for Neven = 0.
What is your age and where are you from however I am from india student of 10 th standard
Good work
For the final answer, it should be noted that you can choose ANY base for these logs BUT the base should be consistent.
These type of questions come in JEE MAIN, I got quite similar question in my march attempt.
What day, what shift?
JEE MAIN??, what's that??
Brilliantly explained!
So simple thnk you sir
Hii friend
I like your video.
You are making good video and explaination is very splendid
Hello teacher, this case there is a relationship between 6 and 9 , so we can use substitution , what if there is no relationship , like 7 and 9
Hello dear, in that case we may not use this substitution method. We'll have to take a different approach to handle that kind of problem. I'll try to touch the base on that kind of problem as well. Thanks for asking. You are awesome!
Take care dear and stay blessed😃 Have a very happy and blessed New Year!
I would automatically apply log without and substitution and simplification which solves your question.
@@Dawlada "log without"? what's that?
In the end, when you have the log raport, I think it would look better to write it as log base 3/2 of (1+sqrt(5))/2
Yes bro, but for other who may be don't know , he calculated a simplified value
Indians are really good in explaining Math. Thanks!
Can't we use logarithmic function at the beginning itself
No, because you will have Ln(a^x + b^x) and that is not equal to xLn(a+b)
@ 4:18 how do you know it's going to be a positive value?
That was awesome👍😊👏👏👏👏
Superb.
Do you also use a calculator for logarithms?!
It's a question of the book, Problems in mathematics by v.govorov.
You are not famous but you are famous by your explanation....
As soon as I saw "1 + u = u^2" I knew u = Phi, the Golden Ratio. So the most exact answer (infinite precision) is ln(Phi)/ln(3/2), or "logarithm in base three halves, of the Golden Ratio"
I was going to mention that (the golden ratio)
Thank you so much for this video take care and stay safe
Thanks Banaz! You are awesome as usual!
How about your injury? You are always in our thoughts and prayers!!!
Have a very happy and blessed New Year!
@@PreMath I am find and don't take much tension for me take care of yourself and stay our connect
You explained it very clearly 👍👍
Thank you so much for your continued love and support. Take care dear and stay blessed😃 Keep smiling😊 Enjoy every moment of your life 🌻
Very helpful! Thank you!
I'm a 68 yr. old man who was never able to pass an algebra class in college. I tried and failed three times. I've been trying to exercise my brain now that I'm retired and have been tackling algebra/math tutorials here on RUclips. I had to stop this video at the 6:40 mark...totally lost and confused! Just like when I was in school some 48 yrs ago when our class got to the using the Quadratic Formula to solve problems I was done...lost and never able to recover. Wondering if there is a teacher on this planet that can teach a person like myself who doesn't seem to possess any significant math skills. My brain fights this stuff tooth and nail.
If you have problems with math try start from the beginning and learn from there you know basic math and built your math skills up then it becomes easier to understand how to read quadric formula And other types of math it’s not easy to learn math because you have to use a lot of times to practice the brain to understand what to do step by step
X1= log(1.618) to base (3/2)... that's all
X1= 1.1868
A thumbs up and a thank you from me
Apply log to both sides from the start.
Great!!! But, at last we needed a calculator...
Though couldn't get the exact value.
The method is amazing...🆗🤓
If u want to get the exact ans...see my response
@@zitachan1216
😇😇😇😇😇😇🤔🤔🤔🤔🤔🙃🙃🙃🙃🙃🙃🙃🙃🙃
Good idea
Many many thanks Idriss
Thanks for the visit! You are awesome 👍 Take care dear and stay blessed😃 Kind regard
@@PreMath you're welcome
Answer x= 1.18681
4^x + 6^x = 9^x
4^x/6^x + 1 = 9^x/6^x ( divide both sides by 6^x)
(2/3)^x +1 = (3/2)^x
introduce y= (2/3)^x, therefore 1/y= (3/2)^x
hence y + 1 = 1/y
y^2 + y =1 ( mutliply both sides by y)
y^2 + y-1 = 0
using quadratic formulae calculator y= 0.618034 and -1.61803
Therefore (2/3)^x = 0.618034 ( I won't use -1.61803 since will log both sides, and the natural log of a negative number is undefined)
x log 2/3 = log 0.618034
-0.176091 x = -0.208987
x = 0.208987/0.17091 (since both were negative numbers)
x = 1.18681 Answer
Wow, that was outstanding. Thank you.
Please make a video on real life use of limits , mathematical induction,complex numbers
Thanks teacher 🇰🇭
My goodness, as you say it's so very easy!
At 8:10 why you did not just remove "Log(2)" in top and bottom?
Because in general, (a-c)/(b-c) does not equal a/b.
@@josephcsible Thank you for clarify, I did not noticed this rule.
Sir why can't we use quadratic equation formula in every quadrantic equation.
great I can refresh my precalculus memory
So nice of you dear! You are awesome 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Take care dear and stay blessed😃
Very good !
The answer is actually 1.1875 by removing x and using relativity on remaining values, this is the easy answer than all of this.
What is the relativity ?
Wow👍 I understood that very well ☺️
I am your regular viewer ,I have a comment ,why don't you describe or give a little literature view before solving equation and add some question for us to test ourselves?
OK, so the proof. 4x = 4 * 1.186 = 4.744. 6x = 6 * 1.186 = 7.116. therefore 4x + 6x = 11.86. Divide 11.86 by 9 and you get 1.317 not 1.186. am I missing something?
Yes you are missing something lmao
You missed too many maths classes.
에이~계산이 잘못되었심다..승수를 곱셈으로 하셨군요?
4^1.186=5.17658
6^1.186=8.37312
9^1.186=13.5435
5.17658 + 8.37312 = 13.5497 그러므로 거의 13.5435 //// 감사하므니다~~
@@om_WHAT Thank you. You've made it so clear.
@@mgbgth5097
아닙니다..
제가 괜히 아는체를 했습니다. 죄송합니다.
항상 즐거운 나날이 되시길 기원합니다.^^
Very interesting!!!❤
This is a special case which works only with the right numbers. So what to learn here?
Use Excel and you don’t need to worry about the special cases. Brute force and ignorance method is a valid and quick way of soloving messy equations.
Right. More useful to learn Newton's method (iterative computational), which can solve almost any such equation.
@@gibbogle The reason I was pointing this out is because it is symptomatic for both RUclipsrs and scientists. Too many scientists of today have no interest in discovering, inventing, learning or understanding anymore. They want to stand in front of a camera and perform tricks like a wizzard. They dont want people to learn or understand anything. They just want you to stand there with open mouth and say Oohhhh, Ahhhh, look at these magicians. As funny as it may seem, this is a catastrophic development.
Thank you sir
Thanks Gowri! You are awesome as usual!
Have a very happy and blessed New Year!
Here I'm sitting in my holiday watching log videos...engineering jokes...study, sleep, girlfriend...pick one, you don't have time for the others🙈 good video, thank you.
It's solution is ascribed to the log function. 🌻
This is for what grade?
Buen trabajo.
Why did you ignore the negative valua?
last 3 Steps எப்படி log value therium? TNPSC exam la log table not allowed
you could also convert it to the form of x² + xy = y²
Why the negative value of u is ignored? What's the reason
thank you so much
Beautiful!
So nice of you Soulemane! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Take care dear and all the best😃 Have a very happy and blessed New Year!
Can you please explain why you divided by 4x and not the other values..how do you know which value to choose or what determines which value you choose..secondly..why is u only a positive value after you solved the quadratic equation..thank you
1. To cancel out at least one power tag (4x) - just simplifying. 2. Because 3/2 doesn't have a power what equals to negative number.
When doing calculation, better use 4 decimal places or 4 significant figures so that the answer is much more accurate.
Hello,
Would you please explain me something please : You have divided by 4 ^X all the member of the equation so 4^X is the denominator but why you don't have multiply by 4^X the numerator ?? (4^X*4^X) / 4^X
Sorry for this silly question. :)
If we are just using a calculator at the end, can't we just graph 4^x + 6^x = 9^x?
Glad I solved it in first attempt now my answer got verified thank you❤ sir
Excellent
sir, I want to learn the intermediate syllabus..because I want to start tuition classes for them in the coming year..can you help me in this regard
I always benefit from you.
Kalau lihat diberanda jadi pengen liat video ini terus 😁
Achei bastante complicado, mas com seu auxílio consegui entender
Anyone knows about the application or tool or platform to write on by hand like this?
Can these type of questions come in the class 10 board?
A geate example of why I use Excel to solve this type of problem. I create an Excel formula with the value of X in one cell with a starting value and a modified version of the equation equaling zero in another. Then I use Excel’s solver function. Done in one minute. The only issue is sometimes you get the wrong root. Then you start with a different value of X. I get paid to get the right answer and not by how I got the right answer.
Let: (2^x )be (a), let (3^x )be( b) , then a^2 +ab -b^2=0, use casio 50FH or3650P2" fmla 01" to solve, a=0.618033988b , (reject the -1.61..),then (2^x)=0.618033988(3^x) , then x=(log0.618033988)÷(log2-log3)=1.186814393 ( exactly), just use calculator 1 step to solve x
What is the base in authors log calculation ?
lets say
“log(2)” ???
I remember LN() or LG()
the bases are “e” and “10”
when you divide through with 9 power x, as the first step, instead of 4 power x, it will give a perfect quadratic equation. However, the roots derived from that result in a completely different answer. x=3.880. I would love to have someone help me to understand that.
Your approach is good and does yield the correct answer of approximately 1.186. (I worked the problem as you suggested just to check the answer again.) So, I got (2/3) power x = ((-1 + sqrt(5))/2). After taking log of both sides and applying properties of logs, x = (log(-1 + sqrt(5)) - log(2)) / (log(2) - log(3)). If this was your result, too, try inputting into your calculator as I have typed out with parentheses or break down the expression into smaller and smaller pieces using approximations. Your answer may be a little different as you introduce rounding error, but you will see that you have chosen a correct method which should yield the same answer.
Wrong
Square root 5 +1 = 3.236 instead of 3.326
Did you notice that the quantity u here is phi, the golden ratio!
I suppose complex solutions for x are excluded.
How can 10x = 9x? 4x + 6x = 10x, If x = 1.186 then 10 x = 11.86. 9x = 9 times 1.186 = 10.647. If I had $1000 in the bank and the bank manager told me that it was actually $900 I'd be a bit annoyed.
What would be a Practical "Real Life" application of this?...
...well...I was thinking more like; Determining hypothetical Gas flow in non Euclidean Universe....
Love how you show all the steps so it's easy to look back on your process, ^oo^
That was immersive.
i would like to watch you solve a problem with you seeing it for the first time..
How does ((3/2)^x)^2 happen?
Can you use the associative law to rewrite the equation 9x+1x=9x then subtract 9x from each side of equation 1x=0 don't know haven't been in school or 45 yard tho maybe
Years
Why do you put just log? Every log must have a base -- log [e] (ln), log [10] (lg) or smth else. There cannot be just log on no base.
Because log always means log[10]. If you want a different base, then you write the base number.
@@mikenajera8834 Maybe this is true for the US math traditions... Here in Russia, if the log at the base of ten (10) is implied, we put it as "lg" (two chars), whereas "log" (three chars) is a logarithm of any valid base (except "10" and "e").
@@creounity thanks for sharing, glad I learned something today 👍
Good problem. It's a tricky one because you can't guess and check! And no integer solutions
I think about you will not use calculator but you did