## anonymous one year ago evaluate the logarithm. log5 (1/25)

1. Kainui

@Jhannybean

2. Jhannybean

$\large \log_a (x) = \frac{\log_b (x)}{\log_b (a)}$

3. Jhannybean

@Kainui

4. anonymous

(1/25)/5????

5. Jhannybean

close, where are your function denotations?

6. anonymous

what do you mean?

7. Kainui

Well I wouldn't use that, I'd use the fact that: $\log_5(\frac{1}{25}) = \log_5(5^{-2})$ and so log base 5 asks us what exponent is on 5? that exponent is -2, so the answer is -2.

8. Jhannybean

$\log_5 \left(\frac{1}{25}\right) = \frac{\log\left(\frac{1}{25}\right)}{\log(5)} = \frac{\log(1) -\log(5^2)}{\log(5)}=...$