Answer
a.) $\log_3 10 = 2x$
b.) $\log 0.1 = -4x$
Work Step by Step
$Express$ $the$ $equation$ $in$ $logarithmic$ $form:$
a.) $3^{2x} = 10$
b.) $10^{-4x} = 0.1$
Exponential form to logarithmic form: $b^c = a \rightarrow \log_b a = c$
a.) $3^{2x} = 10$
Plug in 3 for b, 2x for c, and 10 for a
$3^{2x} = 10 \rightarrow \log_3 10 = 2x$
b.) $10^{-4x} = 0.1$
Plug in 10 for b, -4x for c, and 0.1 for a
$10^{-4x} = 0.1 \rightarrow \log_10 0.1 = -4x \rightarrow \log 0.1 = -4x$
