Hi I have no idea what he is trying to do here it seems like he is trying to reduce everything to the same base number of 3. But if I replace the 3's with a 7 and the 81 with a 49 (which is 7²) It falls apart. What is the stuff I am missing here? I understand the concept of negative exponent and I have a good understanding of how to work with exponents, but as soon as an unknown becomes the variable I just don't get it. And I wonder why the heck I would ever need this.
You have been so helpful with all of your videos. Without you I would not have been able to complete some of my precalculus homework. Your ability to make videos that explain the process used to solve problems in a very clear and easy to follow way is amazing. Thank you so much for helping me and thousands of others with our homework.
For the first one I split 3^(x + 2) into 3^x * 3^2 like you did to get (3^x * 3^2) + 3^x = 10/81 Then I let u = 3^x Which now becomes (u * 3^2) + u = 10/81 3^2 = 9 So it is now (u * 9) + u = 10/81 Which is written as 9u + u = 10/81 Which can be written as 10u = 10/81 Divide both sides by 10 to get u = 1/81 Remember u = 3^x so 3^x = 1/81 81 can be written as 3^4 so you have 3^x = 1/(3^4) Aha! This is the reciprocal of 3^4! Which means we can write this as 3^-4 as a negative power means the reciprocal of the same number with the positive power. So 3^x = 3^-4 Bases are same so powers must be same x = -4 Proof: 3^(-4 + 2) + 3^(-4) = 10/81 3^(-2) + 3^(-4) = 10/81 1/9 + 1/81 = 10/81 1/9 = 9/81 9/81 + 1/81 = 10/81 10/81 = 10/81 OK
@@edo17b i taught myself maths and pre algebra by Openetax and elementary algebra also by Openstax taught me til 10th grade. I really recommend it. If u want more than 10th grade There is pre calculus, intermediate algebra, algebra and trigonometry…etc (literally everything u have difficulty with, openstax is gonna help)
Bruh when i had a test on this a few years ago i desperately scoured your channel searching for a video on this. And now the video is here when i already understand it smh. I appreciate all the videos you make tho mate. All the best.
Answer x =-4 3^x + 2 + 3^x = 10/81 3^x + 3^2 + 3^x = 10/81{3^x + 2 can be expressed as 3^x + 3^2 or 3^x + 9} 3^x (9 + 1) = 10/81 {factor out 3^x) 3^x(10) = 10/81 3^x = 1/81 ( mutliply both sides of equation by 1/10) 3^x = 3^-4 { since 3^4= 81 then 1/81= 3^-4. Could stop here since the base is the same, so x=-4 xlog 3 = -4 log 3 (log both sides of the equation) x= -4 (divide both sides by log 3) Answer x=-4
@the root-coefficient relationship calm down, I just asked if you knew, because I'm new here and I just wondered, i also gonna be watching his videos to learn something :)
I have no idea what you are saying here. I get that 3 raised to the x + 2 is the same as 3 raised to the x power then you multiply by 3² or 9 but where did you get the one and why doesn't this work if I made the 3s a 7 and the 81 a 49. (49 is expressed as 7². and it seems like you are trying to simplify this down to the same base number but then you end up with 50/10 * 7^x which doesn't cancel out or have the same base)
Everyone who doesnt understand math has skill issues. Skills are made by practicing, and those who dont have skill in math just dont practice properly.
1:31 You mean, a POWER of 3, not a MULTIPLE of 3? We are looking for powers of 3 here, not multiples of 3 right? 3:57 The 10s still cancel out even when you didn't divide the ten. You really didn't need to divide both sides by 10 at this time. 5:00 To not have to add fractions, I would multiply both sides of this equation by 81, which is 3^4, then you will have a very easy journey!
@@gibsonigano1847 Well, it's just exponential rules and knowing that you can write the same number in different ways (or that some operations are equivalent, for example multiplying some number for 1/3 is the same as dividing that number by 3).
My simple solution is this. 3^(x+2) +3^x=10/81or 10×81power minus 1.now taking 3^x as common we get 3^x(3^2+1) =10×3^--4.now by comparison we get 3^x=3^--4 or x=--4.
it can help to the other who have already know about it.. but to the other who want to know the all parts specially the way he get the answer of 3 to the fourth power.. i dont know if he factored it but i cant get it in that part.. btw thanks anyway🤦
Answer x= -4 let y=3^x then the equation = (y)3^2 + y = 10/81 (since 3^x + 2 is the same as 3^x multiply by 3^2 or 9 x 3^x, so if 3^x is replaced by 'y' then it becomes 9y) 9y + y =10/81 10y = 10/81 y = 10/81 x 1/10 y = 1/81 or 3^-4 (since 3 exponent 4 = 81 then 1/81 will equal 3 exponent negative 4) 3^x = 3^-4 x = -4 the answer
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Hi I have no idea what he is trying to do here it seems like he is trying to reduce everything to the same base number of 3. But if I replace the 3's with a 7 and the 81 with a 49 (which is 7²) It falls apart. What is the stuff I am missing here? I understand the concept of negative exponent and I have a good understanding of how to work with exponents, but as soon as an unknown becomes the variable I just don't get it. And I wonder why the heck I would ever need this.
this man deserves all the subs!
You've single handedly saved me, several times thank you
You have been so helpful with all of your videos. Without you I would not have been able to complete some of my precalculus homework. Your ability to make videos that explain the process used to solve problems in a very clear and easy to follow way is amazing. Thank you so much for helping me and thousands of others with our homework.
wow, you are amazing. Such simple explaination. loved it
Literally every person I know studies from you. GOAT!!
For the first one
I split 3^(x + 2) into 3^x * 3^2 like you did to get (3^x * 3^2) + 3^x = 10/81
Then I let u = 3^x
Which now becomes (u * 3^2) + u = 10/81
3^2 = 9
So it is now (u * 9) + u = 10/81
Which is written as 9u + u = 10/81
Which can be written as 10u = 10/81
Divide both sides by 10 to get u = 1/81
Remember u = 3^x so 3^x = 1/81
81 can be written as 3^4 so you have 3^x = 1/(3^4)
Aha! This is the reciprocal of 3^4! Which means we can write this as 3^-4 as a negative power means the reciprocal of the same number with the positive power.
So 3^x = 3^-4
Bases are same so powers must be same
x = -4
Proof:
3^(-4 + 2) + 3^(-4) = 10/81
3^(-2) + 3^(-4) = 10/81
1/9 + 1/81 = 10/81
1/9 = 9/81
9/81 + 1/81 = 10/81
10/81 = 10/81
OK
Nice solution
Who taught you math? Or do you read any special math books?
@@edo17b i taught myself maths and pre algebra by Openetax and elementary algebra also by Openstax taught me til 10th grade. I really recommend it.
If u want more than 10th grade
There is pre calculus, intermediate algebra, algebra and trigonometry…etc (literally everything u have difficulty with, openstax is gonna help)
Bruh when i had a test on this a few years ago i desperately scoured your channel searching for a video on this. And now the video is here when i already understand it smh.
I appreciate all the videos you make tho mate.
All the best.
Lucky me :)
Lucky me
lucky me
@Aesthetic because 3 to the power x is the same thing as 1 multiplied by 3 raised to x
MR. Organic Chemistry Tutor, thank you for explaining and solving Exponential Equations.
Thank you so much TEACHER.
** SIR
You are an excellent teacher, and I will always watch your videos
Answer x =-4
3^x + 2 + 3^x = 10/81
3^x + 3^2 + 3^x = 10/81{3^x + 2 can be expressed as 3^x + 3^2 or 3^x + 9}
3^x (9 + 1) = 10/81 {factor out 3^x)
3^x(10) = 10/81
3^x = 1/81 ( mutliply both sides of equation by 1/10)
3^x = 3^-4 { since 3^4= 81 then 1/81= 3^-4. Could stop here since the base is the same, so x=-4
xlog 3 = -4 log 3 (log both sides of the equation)
x= -4 (divide both sides by log 3) Answer x=-4
No
Nice
Thanks for the help. I'm so relieved
I love the way he teaches.
Bro's been helping🔥
Excellent tutorial!
Thank you teacher, with your teachings i really get clear understanding what a gem 💎
This guy is a genius
Look how he is simplifying the gist
iam ❣ pleased with your teaching style
Amazing..sir ..
Thankyou lots of love and respect from India...🇮🇳🇮🇳🇮🇳
Thanks my must teacher
This was amazing. Thanks so kindly.
You have made it more complicated. It can be solved in a easy way. 3^x(3^2+1)=10/81
3^x=1/81=1/3^4
X= -4
Exactly what I was looking for
Am that noob that'd use logarithms but nice video on the alternative method.
You're a genius let's goooo!
@the root-coefficient relationship do you know his age? He sounds like he cant be over 30
@the root-coefficient relationship calm down, I just asked if you knew, because I'm new here and I just wondered, i also gonna be watching his videos to learn something :)
Where did we get the 4 and 5 from?????
I owe u my whole academic life😭
thanks, my question, what application do you use to work on it? thanks
Thanks teacher
I love you mister chemistry tutor
This is so Helpful
Thanks Mr J 😌👍👍
May god bless you teacher
I have no idea what you are saying here. I get that 3 raised to the x + 2 is the same as 3 raised to the x power then you multiply by 3² or 9 but where did you get the one and why doesn't this work if I made the 3s a 7 and the 81 a 49. (49 is expressed as 7². and it seems like you are trying to simplify this down to the same base number but then you end up with 50/10 * 7^x which doesn't cancel out or have the same base)
Lost… I’ll never get this
Real
Skill issue tbh
Everyone who doesnt understand math has skill issues. Skills are made by practicing, and those who dont have skill in math just dont practice properly.
You can do it bro is just 81745 hours of studying
There’s a much simpler solution, split 10/81 into 1/81 and 9/81 (or 1/9) then convert to index form and you can see easily the answer
Thanks teacher 👍
What of a situation where it is 2^x - 2^4-x =0
Got ittt🎉🎉🎉🎉🎉❤
Tysm❤❤❤❤
where'd you get that 1 from?
3 to the power of zero is 1
every variable has a coefficient of 1
I understand every rule and every step I just dont know what or when use them
I'm slightly confused, where does the other 3x go at 2:40 ?
you just saved my life
why do you have to put 1 on 1.3^x?
So helpful.. thanks slot🤪
What if 2x is together?
Ya like im confused
(3^2)^x
3^x*3^x
Thank god logarithms exist
very well explained
Why multiply the first fraction by 9/9 at the end?
To make the denominator the same
excellent work your work is best.
Super!!! Thank you!!!
1:31 You mean, a POWER of 3, not a MULTIPLE of 3? We are looking for powers of 3 here, not multiples of 3 right?
3:57 The 10s still cancel out even when you didn't divide the ten. You really didn't need to divide both sides by 10 at this time.
5:00 To not have to add fractions, I would multiply both sides of this equation by 81, which is 3^4, then you will have a very easy journey!
How can you cancel 10 by not dividing it of course you can cancel it just in your mind but to cancel it you need to divide it smh
By taking the 10 to the other side it'll become - 10 hence they cancel without division
@@sleepywrists380 That's not how math works.
thanks you so much teacher 🙏❤️️🌷🌹
Thank you❤️
How can l find n
(1/2)whole power n=4 to the power of n+1
Amazing my guy
Thank you mister
Really nice explaination ,thumbs up.
I'm lost😢 what happened to the other 3^x...please find me
yeah
you are a wizard
Why do we divide by 10
what happened to the plus sign?
can you please solve these two problems? Cube root of (x^16 y^4 z^21). and fourth root of(X^24. y^10. z^5)
Where the one comes from
Use log on both sides
Thank you.
GOD TIER EXPLANATION
Why are you able to put the 10 • 3^-4? Wouldn’t the 10 go in the denominator and be 3^-4/ 10?
Late but it's because 10 • 3^-4 =10 • (1/3^4)
@@axlrose5082 hi, may I ask like the name of the topic for further explanation why we need to do that like that?
@@gibsonigano1847 Well, it's just exponential rules and knowing that you can write the same number in different ways (or that some operations are equivalent, for example multiplying some number for 1/3 is the same as dividing that number by 3).
@@axlrose5082 thank you very much!!
Thank you
nice video
And why 3^x + 3^x is 3^x?
X=-2,2 add.solution 3/-x=3x3x3=81 ,x+2=-2+2=0 so 1+9=10,/81
Love you teacher
My simple solution is this. 3^(x+2) +3^x=10/81or 10×81power minus 1.now taking 3^x as common we get 3^x(3^2+1) =10×3^--4.now by comparison we get 3^x=3^--4 or x=--4.
Oh thank you so much i love you
Hi. How can i contact with you for i can ask you?
it can help to the other who have already know about it.. but to the other who want to know the all parts specially the way he get the answer of 3 to the fourth power.. i dont know if he factored it but i cant get it in that part.. btw thanks anyway🤦
X=-4 answer
Can someone pls explain to me how did he get the 10?
he added the coefficient
Thanx
Did it in 2 steps
Answer x= -4
let y=3^x then the equation =
(y)3^2 + y = 10/81 (since 3^x + 2 is the same as 3^x multiply by 3^2 or 9 x 3^x, so if 3^x is replaced by 'y' then it becomes 9y)
9y + y =10/81
10y = 10/81
y = 10/81 x 1/10
y = 1/81 or 3^-4 (since 3 exponent 4 = 81 then 1/81 will equal 3 exponent negative 4)
3^x = 3^-4
x = -4 the answer
i got => (ln 10 - ln 243)/ln 3
Confused 😭
x=-4, very simple
In Turkey that's nothing for middleschool students
Nah this question too ez. I solved ans in my head as soon as I saw the thumbnail. X=-4
Nice
My guess is x= (-4)
X=-4
x=négatif4
I'm so lost...
took me 12 seconds by looking at the screen.
the easiest question ever!
i do it😀
X=-4
Easy man
im still a bit confused :/
🙏🙏🙏🙏🙏🙏