Answer
a.) $\frac{1}{9}$
b.) 3
Work Step by Step
$Use$ $the$ $definition$ $of$ $the$ $logarithmic$ $function$ $to$ $find$ $x:$
a.) $\log_3 x = -2$
b.) $\log_5 125 = x$
a.) $\log_3 x = -2$
Rewrite the logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$
$\log_3 x = -2 \rightarrow 3^{-2} = x$
$x = 3^{-2} \rightarrow x = \frac{1}{3\times3}$
$x= \frac{1}{9}$
b.) $\log_5 125 = x$
Rewrite the logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$
$\log_5 125 =x \rightarrow 5^x = 125$
Rewrite 125 as $5^3$ [Note: $5^3 = 5\times5\times5 = 125$]
$5^x = 5^3$
$x = 3$
