anonymous
  • anonymous
Calculus 1 homework. please help!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[6\log_{3}X=-3 \] in equivalent exponential form
anonymous
  • anonymous
You have to isolate the log first
anonymous
  • anonymous
@thearcane do I divide by 6 on both sides?

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anonymous
  • anonymous
Yep.
anonymous
  • anonymous
okay. what do I do next?
anonymous
  • anonymous
And then you know that if \[\log_{a}X = b \] So \[a^{b} = X\]
anonymous
  • anonymous
First of all, you can pass the 6 as exponent of the logarithm argument, in this way it becomes: \[x^6\] Then, you can apply the template (call it "formula" if you prefer) to transofrm a logarithm in the equivalent exponential form: \[log_a{b} = c \rightarrow a^c = b \] In this way, your expression becomes: \[log_3{x^6} = -3 \rightarrow 3^{-3} = x^6\] Solving to find the x: \[x^6 = \left(\frac{1}{3}\right)^3 \] \[x = \frac{1}{\sqrt{3}}\]
anonymous
  • anonymous
These are my answer choices \[x ^{6}=-10\] \[x ^{6}=27\] \[x ^{3}=\frac{ 1 }{ 27 }\] \[x ^{3}=10\]
tkhunny
  • tkhunny
I'm a little puzzled why we ever would see \(x^{6}\) in the solution to this problem. We have a beautiful logarithm simplification, why not use it? \(6\cdot log_{3}(X) = -3\) Notice how the Domain is X > 0. If we do this (log rule): \(log_{3}\left(X^{6}\right) = -3\), we have introduced Domain that wasn't there, before. This is how the solution above was slightly incorrect along the way. \(x^{6} = 1/27\) has more than one solution - all of which must be evaluated for appropriateness. If instead, we do this (division): \(log_{3}(X) = -3/6 = -1/2\), we're still on the right track, having NOT changed the Domain, and solution is trivial, \(X = 3^{-1/2} = \dfrac{1}{\sqrt{3}}\) Not really seeing that in the answer choices. Are you SURE you wrote the problem statement correctly?
anonymous
  • anonymous
6⋅log3(X)=−3 I have to write this problem in exponential form
tkhunny
  • tkhunny
That has been done, above. Not sure what the answer sheet wants.
anonymous
  • anonymous
All of you guys are right! thanks for your help. sorry this site I'm on is really weird

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