Question

evaluate \\(\log_{5} \frac{1}{625}\\). \\(\log_{5} \frac{1}{625} = \square\\)

Explanation:

Step1: Rewrite denominator as power of 5

$625 = 5^4$, so $\frac{1}{625} = 5^{-4}$

Step2: Apply logarithm power rule

$\log_{5}5^{-4} = -4\log_{5}5$

Step3: Evaluate $\log_{5}5$

$\log_{5}5 = 1$, so $-4 \times 1 = -4$

Answer:

$-4$