How do I find x? Exponential equation with two different bases. Reddit precalculus r/Homworkhelp
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- Опубликовано: 29 сен 2024
- Learn how to solve an exponential equation with two different bases. We will go over two ways. Be sure to remember the rules of exponents and logarithms. Here's a video with 10 examples of solving exponential equations, from basic to hard!: • How to solve exponenti...
This question is from Reddit r/Homeworkhelp / ik4bneuk6y
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#math #algebra #mathbasics
Here's a video with 10 examples of solving exponential equations, from basic to hard!: ruclips.net/video/K8CQbSD9wis/видео.html
I'm just impressed how you write with two different colors in one hand.
Imagine now how sex
it's like using chopsticks
You must be special
Lmao exactly the same I commented about two weeks ago
I'm impressed that you do that with two hands
i took precalc 4 years ago and was arbitrarily recommended this video yet I still feel compelled to do the homework this man has given
I took it 15 years ago and I still watch these videos because it feels like a waste of effort to learn all of that an forget it. 🤷♂️
"How to find X?"
Bro, it's time to move on. Your X doesn't care about you anymore.
y?
@@bprpmathbasics😂 thats good
Lol. Bro got owned by Math😂
Don't you z how pointless it is?
lol
I solved it slightly different. I recognized that 3^(x+1) can be rewritten as [(1.5)(2)]^(x+1), which can be expanded as 1.5^(x+1) 2^(x+1). This is very helpful as it gives us an exponential of base 2 on both sides of the equation, which allows us to cancel out the x on the left side through exponent division rule. The full solution is below:
2^(x-5) = 3^(x+1)
2^(x-5) = [(1.5)(2)]^(x+1)
2^(x-5) = 1.5^(x+1) 2^(x+1)
2^(x-5)/2^(x+1) = 1.5^(x+1)
2^(-6) = 1.5^(x+1)
Now we only have a single x variable to deal with, so we could simply apply log to both sides and isolate for x
log[2^(-6)] = log[1.5^(x+1)]
(log[2^(-6)]/log[1.5]) - 1 = x
-11.257 = x
Well done
when i saw the thumbnail i guessed that since 2^(x-5) = 3^(x+5)
we can do something like 2^(x-5) . 1/ 3^(x+5)
then 2^(x-5) x (3^(x+5)) ^(-1)
and go on i guess . Btw im in ninth grade so i have no clue about what ln is
nice is the antilog required or this is it.
ln is called natural log, where the base is 'e' which is called eular constant. BTW which country do you belong to
I got that too, thanks for making me feel like I wasn't alone 😂
So I'm a 3rd year medical student watching this video and I dearly enjoyed it. Its like going down the memory lane. Really smooth teaching. Kudos to you..❤
Hope the clerkship is treating you well.
@@kaideng2571 yup, thanks. Have a good day.🫂
I Just Saw the Thumbnail And Thought " Ehhhh That looks Ez Lets Just Do It " Only to waste 30 mins And Find Out It Have Logarithm Which I Havent Studied😂
I wasn't taught log at school at all. I had to look it up online. Even though we hadn't had proper knowledge about log we still have to use in calculus
Lol same💀
guys we can solve it in another way too.
what i did was this:
i took log on both lhs and rhs. so the exponent comes down and the equation becomes like such
(x-5)log 2=(x+1) log 3
now we know log 2= 0.3010 and log 3=0.477 so we just use those values in the equation
(x-5)*0.3010=(x+1)*0.477
0.3010x-1.505=0.477x+0.477
this becomes
-0.176x=1.982
x=1.982/-0.176
x=-11.26
It was not log tho. It's was ln.
@@MetimbersShivered works w log too
@@MetimbersShiveredyeah you'd have to multiply it with 2.303 to convert ln to log
That'd be easier ig
@@Gaysandthechaos yes
@@MetimbersShivered, in this scenario, either 'ln' or 'log' is acceptable. This is because the bases of logarithms would get cancelled in the process as long as the bases are the same.
oh my fricking god how many whiteboard pen boxes do you have😂
Been watching since gr7 and was so frustrated I couldnt understand any of these but now in gr10 im proud to announce I finally can:D
This is very brilliant!
As a student going into my sophomore year next year I am quite happy that I understood all of this!
i somehow went through algebra I and II, precalc, calc I and II, yet never saw any of this and now i feel like i was robbed. this looks so interesting and i am now lamenting never having had a math teacher that makes math interesting. thanks, random math guy on the internet!
Same story🤷♀️
I have a doubt!
At the step (x-5)ln2=(x+1)ln3
Can't we Directly substitute the value of log 2 and log 3 in the eqn?
As a sophomore in College math, this actually makes sense
I figured immediately it was gonna be complicated because (although I could be wrong) there is no integer exponent of 2 that is divisible by 3
That's right -> Just express any exponent of 2 in terms of primes, you will never have the number 3. The same is true that no exponents of 3 are divisible by 2 for the same reason.
I solved it in a similar way somewhat. Started with taking the natural log but instead grouped terms like:
(x-5)/(x+1)=ln3/ln2
(x+1-6)/(x+1) = ln3/ln2
1-6/(x+1)=ln3/ln2
(x+1)=-6/(ln3/ln2-1)
x=-6/(ln3/ln2-1)-1
x~=-11.257
That seems more intricate.
This helped me so much, thank you!!!
You are so talented in teaching. Thank you for your wonderful videos.
로그공식 까먹었던 걸 복습하게 되는 영상. 이거보고 다시 생각났네요
Hi in which grade do you learn logarithms in Korea?
@snmnurr people learn logarithms in 11th grade in Korea, but Im now in high school in the US :)
"96... very nice"
Dunno why I laughed so hard at that. But I learned log functions just last year in school and forgot about how fun math is. Really nice vid man!
Thanks u verry much
It's long. You can write it like (2^x)/32=3*3^x from where you can easily go to (2/3)^x=32*3
I am from India and this is the most basic example that we solve in grade 11 🙃🫠
“Okay, let me start with 1 and see if that works…”
…
…
…
“Okay, that didn’t work. I think I’ll try 2 next…”
…
…
…
“Alright, that’s no bueno. How about 3?”
I'm studying medicine. Idk why im here. 😂 but i enjoyed your content.
Thanks!
I don't know if anyone else has pointed this out, but you shouldn't have used x at the end when explaining how to use the change of base rule. It will definitely confuse people who are not very familiar with math as you have an equation for x right next to it on the board.
Why did you not use log table
-Log96/log(1.5)
Love this reddit series
Wow that is much easier than i thought
x = ln(96)/[ln(2)-ln(3)]
Your multiplication signs are so tiny
Bro im 7th grade why did i click on this video🥲
I'm grade 8th , quiet relatable
In on 9th grade i also wonders will im here on this video i guess
I was in 7th grade 17 years ago, wondering why I click the video
As a sophomore doing College math, I agree
To anyone who's planning on taking pre-calc or calculus in the future, the only solution is to practice the everliving hell, there's no other way (I mean same can be said for other subjects, but you get the idea). Much luck for the future!
Better method
Just put different values of x
How hard it can be ? You can see X sitting on top of 2 and 3 ... Why people are finding it difficult to find it ... Hardly took me a second to find
=-11.4
We’ve been looking for x since the 17th century.
I tried and ended up at the point b4 u had to use calculator not knowing that I actually do have to use it thought X could have been solved without calculator
For Asian students, this exercise is quite easy
Can you solve this equation please?
e^(x-1)/x =x
I know that x equals 1, but I did not know how to prove it
-11.25707
I don't know why I'm watching this at 5AM since I'm a physicist doing PhD in neurophysics and computational neuroscience, but I thoroughly enjoyed this. 10/10. Younger generations are so lucky that they have someone like you explaining maths. Hopefully they'll know how to appreciate it and not waste their brains away on TikTok...
Woah..sounds interesting.. can you elaborate like what things you study and tools you use?
Ill take it as a compliment mr neurophysics man
Im a 10th grader that likes math
I'm a physics major as well but haven't taken a math course in a while. He's really helpful for keeping all the concepts fresh in my brain.
Yes brother true
Physics undergrad here, this man (and Organic Chemistry tutor) saved me during calc 2
I'm in 10th grade, so whenever he says "let's use this rule" I'm just like "uh huh"
Edit: it's crazy how different some curriculums are in other countries.
We learned the logarithm in 10th grade😅 (Germany)
Why are u here?
I enjoy watching advanced math, even if I don't understand it fully.
@@Musterkartoffel I'm only half way through the year so I may learn it soon.
SAME FROM INDIA BTW
I have a Zoology exam tomorrow. It's 3am. 10/10
Yo how did it go? 😂
So, how did it went?
It's been 4 months. So, how did it go ?
@@tobedecided8886bro never been seen again after the exam 💀
@@0kiwwihe died after that
Bro i am a Engineering major why did i click on this video
Same thing im like do i really have nothing better to do than to glance at my freshman year history 😂😂
Might be 2 reason..
1. To confirm ur solution thought process
2. Ur too dumb to be an Engineer.
To expand it, you use change of base to get log(96)/log(2/3). When dividing a logarithm, of course, you subtract the log of the denominator from the log of the numerator, which gives log(96)/(log2-log3). We can take the prime factors of 96: 3 and 2⁵, to get log(3•2⁵)/(log2-log3). With multiplication of logarithms, you add the logs of the multiplicands, so (log3 + log(2⁵))/(log2-log3). Finally, with exponentiation, you multiply the logarithm of the base by the exponent, which gives (log3 + 5log2)/(log2-log3).
I should have used ln rather than log, but I'm so used to using log for change of base that I just did that by default. It works the same either way (:
Nicely done, thanks for doing my homework!
you can just use laws off exponents bcuz that seems easier. then you log it at the end for answer
turn 2^(x-5) into 2^x*2^-5 and turn 3^(x+1) into 3^x*3. an example of this is (3^2)*(3^2)=3^4
expand into 1/32(2^x)=3(3^x)
do some division to isolate x as much as possible. 3/(1/32) = 96 or (1/32) = 1/96. End up with 2^x=96(3^x) or 1/96(2^x)=3^x
x root everything. 2=xroot(96)*3 or xroot(1/96)*2=3
more division to isolate x. 2/3=xroot(96) or 3/2=xroot(1/96)
put everything to the x power. (2/3)^x=96 or (3/2)^x=1/96
now log bcuz inverse of exponential to finnaly actually isolate x. log(base(2/3)) of 96 = x or log(base(3/2)) of 1/96 = x
x= ~-11.25
well, how do you get from
log(96)
----
log(2/3)
to
ln(96)
---
ln(2/3)
?
Log(96)/Log(e) is ln 96. Divide by log e in Nr and Dr
Since when did i watch math for entertainment tf
australian here, i used my calculator. ive only seen the thumbnail and came straight here. the answer i got was (-ln(96))/ln(3/2) or approximately-11.257
edit: finished the video now and checked those two values of x. both were equal to my above answer. very nice 👍
I just do log on both side and got the same answer x = -11.25
Bro I'm in 10th grade and I reached (2/3)^x = 96 and was like, "Now what?". Then I realised "Oh, this is out of bounds" 💀💀💀💀
this is 9th grade in Germany
@@imagod4796 I thought Asia had the toughest math.....
@@imagod4796 This is 12th grade in Turkiye (I know it sucks dumb education system) , but I learned it way before because of calc bc.
@@exip9288 We all have shitty educations, here in Romania we learn calculus in 11th grade to 12th grade, they should have system of education like USA, this is where the people can learn it well, we have short time in school but too much to learn, cause it's not just math, its also other lesson that it supposed to be in college like physics, chemistry, etc.
bro but if u have studied from better school in 9th they would have taught u (in india)
bro fumbels my brain and proceedes to say:"but, here is a prettier way to do it"
C'mon dude, if you know the rules of log this is a pretty simple problem.
So maybe they don't know logarithm rules yet. C'mon dude if you can calculate a Hohmann Transfer, this is a pretty simple problem. @@CST1992
@@CST1992 if we know the rules of log we wouldnt be here for an explanation now would we? lmfao
@@celoreads you don't know what log is but you are on a calculus video? Go back to high school... "lmfao"
@@CST1992Do you not realise that the title of the video literally says precalculus?
the second option is always what comes to my mind first, i find it way easier and more intuitive, but ive forced myself doing the natural base method too cuz you have to know them both imo
I do the complete opposite: whenever I see an x as an exponent, I use ln, because the calculator can eventually solve any monstrosity I type in as long as there are numbers 😂
Bringing down the x is my number one priority 🫡
Try this next: 2^x=5^(x+2)
Answer here: ruclips.net/video/WL-npSEyVTo/видео.html
bro really out here assigning hw 💀
(I'm in 8th grade, i dont know shit)
I actually learned this last unit.
2^x=5^(x+2)
xln2=xln5+2ln5
xln2-xln5=2ln5
factor out x
x(ln2-ln5)=2ln5
x=2ln5/(ln2-ln5)
I’m not sure if there’s a better way to simplify it
x=log2/5(25)
@@FloraLemonYTThat's correct! 👍
I mean:
(X-5)log2 = (x+1)log3 … -> x = (5log2 - log3)/(log2 - log3) is just way less complicated than the methods shown, at least this is the standard method in uk
Very first approach of solving exponential equations is using logarithms.
Actually the equation becomes easy, when you use log in exponential problems.
Thanks ❤🇮🇳
I gave up on maths nearly 7 years ago in school. In my post graduation i watch this and feel my antipathy towards the subject reduce a little. Thanks
I'm in 7th grade, so i tried to solve it like this. i know it looks bad and there might be some mistakes here and there, but what matters is i got to the right answer!
2^(x-5)=3^(x+1)
2^(x-5)=2^(log2(3^(x+1)))
x-5=log2(3^(x+1))
x=log2(3^(x+1))+log2(2^5)
x=log2(32*3^x*3)
x=log2(96*3^x)
log2(2^x)=log2(96*3^x)
2^x=96*3^x
(2^x)/(3^x)=96
(2/3)^x=96
x=log2/3(96)
Bro youve studied log in 7th grade? When i was in 7th grade i was busy counting the leaves in my garden trees lol...btw good going
I would consider simplify it with log to the base 10 which yields the same answer as the answer you obtained.
We could write it as,
X-5log(2)=X+1log(3)
Which on further simplification can provide,
x= -6.58/0.58= -11.3
And the answer you obtained at the end,
log (base)2/3 (96)= -11.26 (approx)
I feel its less hectic
That was a really good explanation! Thank you for explaining so clearly! 👏
The only way to watch these videos without pulling my hair out is watching st 2x speed
im in 12th, we learnt this last year, i have my maths test in 1 hour, why am i watching this
The professor when ever I start copying the notes. 3:34
That made me laugh a bit lol
😄
It’s 4:20 am right now and I have no idea why I’m watching this at this time. I told mom to call me at 8 and wake me up. I guess now I have a solid reason to tell her why i was awake.
log(2**(x+5)) = log(3**(x+1))
(x+5) * log(2) = (x+1) * log(3)
(x+5) * log(2) = (x+1) * log(3)
x * log(2) + 5 * log(2) = x * log(3) + log(3)
x * (log(2) - log(3)) = log(3) - 5 * log(2)
x = (log(3) - 5 * log(2)) / (log(2) - log(3))
import math
log2 = math.log(2)
log3 = math.log(3)
x = (math.log(3) - 5 * log2) / (log2 - log3)
print(f"The value of x is: {x:.4f}")
The value of x is: 5.8380
you can do backwords in 6:00 ONLY IF a and b are both positive (theoretically a can be 0 , but it's a disputable question)
что?
@@amanda-we9fv now it's correct. I mean you can't do backwards if a and b are both negative ,roots of a and b won't be defined then, while root of ab will be defined
In this case it is.
If it is positive that means a,b ∈ N
I have a question sir. Why we need to use ln instead of log, or we can use which?
Hi...we can use log in 1st method instead of ln ...i used log and the ans is same, u just need to know values of log2 and log3
@@sonvisharma5264 i see.... Thank you
EASY PEASY LEMON SQUEEZY
By Taking log both sides, power comes to multiply , and then put values of log2 and log3 , then x comes to be -19
Thank you for taking the time to make this video. Much appreciated. ❤
Glad to help! 😃
Immediate reaction is "x is not positive integer, because 2 and 3 are prime, so the prime factorisation of 2^i will never equal that of 3^j, where i and j are any positive integer".
This also works for negative integers, even for non-zero rational numbers. So the only possible rational solution would be if both exponents are zero (at the same time, which is not possible in this case).
You never know if x is a quaternion or is mod |p| or whatever in these dumb questions.
@@deltalima6703This is an algebra channel, not a calculus or analysis channel, so don't overthink it.
Correct
how about taking log on both sides the use the values of log2 and log3 that is 0.3 and 0.47
Students out of India use calculator for passing in their maths exam is that true?
Oh well this was easy I solved the ques withoust using pen.
I played Mario kart tour every day during honors precalc in high school and I regret it every day as an engineering major in university
2ⁿ/32=3ⁿ×3
2ⁿ/3ⁿ=96
(2/3)ⁿ=2⁵×3
Idk what else can I do
2:25 imo you should have transposed the terms to other side respectively instead of subracting/adding on both the sides
Anime Dekhne Vale life mae kuch nahi kar sakte
In the first example, could you have used log instead of ln? When to use log vs ln?
In this scenario, there is not difference. The only situation requiring 'ln' is when the base of an index is 'e'.
Also, ln(x) is equivalent to log(e, x).
to think that I knew all those formulas you used and wrote on right side but still I didn't knew how putting them together will get me the answer. Thanks a lot. Any advice on how I can solve this thing of not knowing when to put and which things together to solve questions like this ?
I'm not sure why I'm clicking on this. I am an economics student and just reading about consumer behavior theory, and it contains Lagranian function, which I've never heard before and try to find wtf is that equation but anyway I'm satisfied with this video.
why did he use natural log, but not log?
Try this:
Find the value of A (A>1) such that
The graph of y =A^x and the graph of y = ln x have only one interesecting point. 😂
Here ruclips.net/video/uMfOsKWryS4/видео.htmlsi=NdNJR8P2ynDqugfr
@@bprpmathbasics I watched that video clip. But it solved the case when both the exponential function and logarithmic function shared the same base, how about when the base of the logarithmic function is not the same as the base of the exponential function?
I m a bio student why am watching this
Great explanation 👍
Could you please make a video on how to find values with decimal exponents
Example) (15) ^1.4
Equivalent answer with slightly less distribution:
2^(x - 5) = 3^(x + 1)
(x - 5) ln 2 = (x + 1) ln 3
x - 5 = (x + 1) log2(3)
x - 5 = x log2(3) + log2(3)
x - x log2(3) = 5 + log2(3)
x = (5 + log2(3)) / (1 - log2(3))
meanwhile me using trial and error to find the answer
I'm in 8th grade... Literally what is this sorcery
I didn't even know that was an "l", I thought it was a capital i 😭
What I like the best about this guy is he still uses a whiteboard and not a smart board
My friends in my old algebra class had a funny way of remembering the ln(x^2)=2lnx theorem. We called it the yeet theorem because you take the exponent and yeet that shit to the front
i just approximated to solve it quickly:
x-5/x+1 = log3/log2
x-5/x+1 = 0.4771/0.3010
10x-50 = 16x+16
x=-11
im pretty sure i got this question in my IMO examination like 2 years ago (8th grade)
These are the only math videos I watch... FOR FUN. actually i hate math (always have), but this asian math god makes it interesting somehow.
I am in 12class, I think it's too easy for 12 class student I solved in just a min
Could you not also do $$log_{2}3=(x+1)/(x-5)$$ ? (LaTeX format)
Okay so I turned the 2 and 3 into 6 so 3x-15 = 2x+2 , x=17 and my answer is wrong but can someone explain why the method is wrong ?
Both answers were equal to -11.25706775. That blew my mind.
I'm an international relations major and somehow watched this whole video and nodded everytime he looked at me as if im getting everything he says
(x - 5)ln2 = (x + 1)ln3
(x - 5)/(x + 1) = ln3/ln2
1 - 6/(x + 1) = ln3/ln2
1 - ln3/ln2 = 6/(x + 1)
1/(1 - ln3/ln2) = (x + 1)/6
6/(1 - ln3/ln2) = x + 1
6/(1 - ln3/ln2) - 1 = x
It's crazy how i first saw the question in the thumbnail and knew that i had to add log on both sides
Why use natural logs when you can just use common logs? I feel like they’re friendlier, since they don’t involve e. That could just be me though.
Dont care about anything except for how he explained moving x from right part of the equation to the left part with the opposite sign 😭
Am I the only one who absolutely loves logs. It’s not that I find them really easy or anything, they’re just so awesome.