Answer
a.) $\log 10,000 = 4$
b.) $\log_5 \frac{1}{25} = -2$
Work Step by Step
$Express$ $the$ $equation$ $in$ $logarithmic$ $form:$
a.) $10^4 = 10,000$
b.) $5^{-2} = \frac{1}{25}$
Exponential form to Logarithmic form: $b^c = a \rightarrow \log_b a = c$
a.) $10^4 = 10,000$
Plug in 10 for b, 4 for c, and 10,000 for a
$10^4 = 10,000 \rightarrow \log_{10} 10,000 = 4 \rightarrow \log 10,000 = 4$
b.) $5^{-2} = \frac{1}{25}$
Plug in 5 for b, -2 for c, and $\frac{1}{25}$ for a
$5^{-2} = \frac{1}{25} \rightarrow \log_5 \frac{1}{25} = -2$
