Question

evaluate each expression.
(a) $log_{6}6 = square$
(b) $log_{4}\frac{1}{64} = square$
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Explanation:

Step1: Use log base identity

Recall $\log_a a = 1$ for $a>0,a
eq1$.
For $\log_6 6$, apply the identity: $\log_6 6 = 1$

Step2: Rewrite argument as power of base

Rewrite $\frac{1}{64}$ as $4^n$. Since $4^3=64$, $\frac{1}{64}=4^{-3}$.

Step3: Evaluate the logarithm

Use $\log_a a^k = k$.
$\log_4 4^{-3} = -3$

Answer:

(a) $1$
(b) $-3$