## marcelie one year ago Help please how do i solve this log equation. Please show me the steps . log 9 (1/729)

1. marcelie

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2. Jhannybean

Change of base formula : $$\log_b(x) = \dfrac{\log_d (x)}{\log_d (b)}$$

3. marcelie

ah okay. is that the same thing as log b(m/n ) = log b M - log b N ?

4. Jhannybean

No.

5. Jhannybean

Just treat $$\frac{1}{729}$$ as $$x$$ :)

6. marcelie

oh okay . Got it :) ty

7. Jhannybean

8. marcelie

i got -3

9. Jhannybean

Awesome!! good job.

10. Jhannybean

This is how I did it

11. marcelie

:)

12. 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}