marcelie
  • marcelie
Help please how do i solve this log equation. Please show me the steps . log 9 (1/729)
Mathematics
chestercat
  • chestercat
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marcelie
  • marcelie
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Jhannybean
  • Jhannybean
Change of base formula : \(\log_b(x) = \dfrac{\log_d (x)}{\log_d (b)}\)
marcelie
  • marcelie
ah okay. is that the same thing as log b(m/n ) = log b M - log b N ?

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Jhannybean
  • Jhannybean
No.
Jhannybean
  • Jhannybean
Just treat \(\frac{1}{729}\) as \(x\) :)
marcelie
  • marcelie
oh okay . Got it :) ty
Jhannybean
  • Jhannybean
So what did you get as your answer?
marcelie
  • marcelie
i got -3
Jhannybean
  • Jhannybean
Awesome!! good job.
Jhannybean
  • Jhannybean
This is how I did it
marcelie
  • marcelie
:)
Jhannybean
  • Jhannybean
\[729 = 3^6, \qquad 9 = 3^2 \]\[\begin{align} \log_9 \left(\frac{1}{729}\right) &= \frac{\log\frac{1}{729}}{\log(9)} \\\ &= \frac{\log(1)-\log(729)}{\log(9)} \\\ & = \frac{-\log(3^6)}{\log(3^2)} \\\ &= -\frac{6\log(3)}{2\log(3)} \\\ &= -3\end{align} \]

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