Using the power rule of logarithms, how can log (1/125) be reweitten?

Question

1)-3log(5)
2)log_{5}(1/3)
3)[log(1)]/[log(125)]
4)5log(1/3)

Answer 1

To rewrite \( \log(1/125) \) using the power rule of logarithms, we can start by expressing \( \frac{1}{125} \) in terms of powers of 5.

Since \( 125 = 5^3 \), we can rewrite \( \frac{1}{125} \) as \( \frac{1}{5^3} = 5^{-3} \).

Now, applying the logarithmic property that says \( \log(a^b) = b \log(a) \):

\[ \log(1/125) = \log(5^{-3}) = -3 \log(5). \]

Thus, we find that:

\[ \log(1/125) = -3 \log(5). \]

This matches option 1:

1) -3log(5)

So the correct option is 1).