Answer
a.) $8^{\frac{1}{3}} = 2$
b.) $10^{-2} = 0.01$
Work Step by Step
$Express$ $the$ $equation$ $in$ $exponential$ $form:$
a.) $\log_8 2 = \frac{1}{3}$
b.) $\log_{10} 0.01 = -2$
Logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$
a.) $\log_8 2 = \frac{1}{3}$
Plug in 8 for b, 2 for a, and $\frac{1}{3}$ for c
$\log_8 2 = \frac{1}{3} \rightarrow 8^{\frac{1}{3}} = 2$
b.) $\log_{10} 0.01 = -2$
Plug in 10 for b, 0.01 for a, and -2 for c
$\log_{10} 0.01 = -2 \rightarrow 10^{-2} = 0.01$
