Answer
a.) $5^{-1} = \frac{1}{5}$
b.) $4^3 = 64$
Work Step by Step
$Express$ $the$ $equation$ $in$ $exponential$ $form:$
a.) $\log_5 (\frac{1}{5}) = -1$
b.) $\log_4 64 = 3$
Logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$
a.) $\log_5 (\frac{1}{5}) = -1$
Plug in 5 for b, $\frac{1}{5}$ for a, and -1 for c
$\log_5 (\frac{1}{5}) = -1 \rightarrow 5^{-1} = \frac{1}{5}$
b.) $\log_4 64 = 3$
Plug in 4 for b, 64 for a, and 3 for c
$\log_4 64 = 3 \rightarrow 4^3 = 64$