anonymous
  • anonymous
2log(x-3)+1 = 5 Could you break it down step by step? I'm a bit confused on how to do this algebraically
Mathematics
chestercat
  • chestercat
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Callisto
  • Callisto
To solve x?
anonymous
  • anonymous
yes, i presume
Callisto
  • Callisto
Okay, first, subtract both sides by 1, what do you get?

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anonymous
  • anonymous
you get 2log(x-3) = 4
Callisto
  • Callisto
Right, now divide both sides by 2, what do you get?
anonymous
  • anonymous
log(x-3) = 2
anonymous
  • anonymous
haha, that's fine :)
calculusfunctions
  • calculusfunctions
Don't mind me. @Callisto seems to be doing a fine job teaching so I'll just observe if you don't mind? I'll only respond if you ask.
Callisto
  • Callisto
Yup! Now, take anti-log for both sides. What do you get? Note: anti-log = inverse of log For example, logx = 1 => 10^(logx) = 10^1 => x = 10^1 = 10
anonymous
  • anonymous
yikes, haha, i'm not for sure. I briefly remember anti-logs but I'm not for sure what do with them
Callisto
  • Callisto
Do you understand that example?
anonymous
  • anonymous
i'm starting to get it. logx = 1. I understand that but not after that
calculusfunctions
  • calculusfunctions
If I may, @Callisto perhaps he'd @Egirl01 would understand if you asked her to change the logarithm form to exponential form. @Egirl01 do you know how to do that.
anonymous
  • anonymous
No, I'm sorry
anonymous
  • anonymous
give me one second
anonymous
  • anonymous
\(\large b^x=y \rightarrow log_by=x \)
anonymous
  • anonymous
log^2 = x-3?
Callisto
  • Callisto
logx = 1 is actually just an example... ---------------------------------- Intuitively, log a number is the value of the power of the base Let say, I have a number 100, which can be rewritten as 10^2 Now, I take log (base 10) of that number (100), so I'll get 2, since 10 to the power of 2 give me 100. (Sorry if I make it even worse...)
anonymous
  • anonymous
No, I understand the piece. so if its simply log, then its naturally log10, and the anti-log of log10 is 1/10 right?
Callisto
  • Callisto
anti-log of log 10 is 10. \[\log^{-1}(log10) = 10\] anti-log is the inverse of log.
anonymous
  • anonymous
Alright. So then it'd be 10 (x-3) = 2?
Callisto
  • Callisto
No.... How did you get that?
anonymous
  • anonymous
the anti-log of log 10 is 10, so log(x-3) = 2 would turn to 10(x-3) = 2? Obviously that is wrong. I'm a bit lost but you can continue onto the next part of solving the equation. I'll eventually figure what I'm doing wrong
Callisto
  • Callisto
\[log(x-3) = 2\]Take anti-log for both sides: \[\log^{-1}(log(x-3)) = \log^{-1}(2)\] Perhaps you can simplify the left first.
anonymous
  • anonymous
I still don't quite follow, but continue on. I'll understand eventually :)
Callisto
  • Callisto
Nope.. It's your turn to work on it... Which part you don't understand ?
anonymous
  • anonymous
how exactly I create the anti-log from log(x-3)
Callisto
  • Callisto
Because you are doing something on both sides... You create anti-log to undo the work of log...
anonymous
  • anonymous
So the anti-log of log10 is 10, right? and the anti-log of 2 is what?
Callisto
  • Callisto
Before answering you question, could you please answer few questions first?
anonymous
  • anonymous
okay
Callisto
  • Callisto
What is log10?
anonymous
  • anonymous
log10 =1
Callisto
  • Callisto
What is log100?
anonymous
  • anonymous
log100 = 2
Callisto
  • Callisto
Can we tell me what number do I have to take log on in order to get 1?
anonymous
  • anonymous
10?
Callisto
  • Callisto
Yes. So, what number do I have to take log on in order to get 2?
anonymous
  • anonymous
100
Callisto
  • Callisto
Yes! How did you get this answer?
anonymous
  • anonymous
because you inversed it?
Callisto
  • Callisto
Yes! So, now, can you answer your question? what is \(\log^{-1}2\)?
anonymous
  • anonymous
It is 100
Callisto
  • Callisto
Yes!
anonymous
  • anonymous
So 10(x-3) = 100?
Callisto
  • Callisto
No. Another set question questions... What is log10 (again)?
anonymous
  • anonymous
log 10 is 1
Callisto
  • Callisto
You got it right for the right side, it's wrong for the left.
Callisto
  • Callisto
What is \(\log^{-1}log(10)\)?
anonymous
  • anonymous
10
Callisto
  • Callisto
Yes. What is \(\log^{-1}(log100)\)?
anonymous
  • anonymous
2?
anonymous
  • anonymous
WAIT
anonymous
  • anonymous
100?
Callisto
  • Callisto
Yes!
Callisto
  • Callisto
What is \(\log^{-1} (log1000)\)?
anonymous
  • anonymous
1000
Callisto
  • Callisto
So, we can see that \(\log^{-1}\) of log a number is the number itself, agree?
anonymous
  • anonymous
yes
Callisto
  • Callisto
So, \(\log^{-1} (\log y) = y\), agree?
anonymous
  • anonymous
yes
Callisto
  • Callisto
So, what is \(\log^{-1} (log(x-3))\)?
anonymous
  • anonymous
x-3?
Callisto
  • Callisto
Yes!
Callisto
  • Callisto
Can you simplify the following now? \[\log^{-1}(log(x-3)) = \log^{-1}(2)\]
anonymous
  • anonymous
x-3 = 100?
Callisto
  • Callisto
Yes! Now can you solve it?
anonymous
  • anonymous
yes
anonymous
  • anonymous
x = 103?
Callisto
  • Callisto
Nice :D and Yes! Do you understand how to solve this type of question now?
anonymous
  • anonymous
yes! Thank you soooo much for your help! I really appreciate it!
Callisto
  • Callisto
You're welcome :)

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