Answer
a.) $\log_4 0.125 = -\frac{3}{2}$
b.) $\log_7 343 = 3$
Work Step by Step
$Express$ $the$ $equation$ $in$ $logarithmic$ $form:$
a.) $4^{-\frac{3}{2}} = 0.125$
b.) $7^3 = 343$
Exponential form to logarithmic form: $b^c = a \rightarrow \log_b a = c$
a.) $4^{-\frac{3}{2}} = 0.125$
Plug in 4 for b, $-\frac{3}{2}$ for c, and 0.125 for a
$4^{-\frac{3}{2}} = 0.125 \rightarrow \log_4 0.125 = -\frac{3}{2}$
b.) $7^3 = 343$
Plug in 7 for b, 3 for c, and 343 for a
$7^3 = 343 \rightarrow \log_7 343 = 3$