## Precalculus: Mathematics for Calculus, 7th Edition

a.) $\frac{1}{9}$ b.) 3
$Use$ $the$ $definition$ $of$ $the$ $logarithmic$ $function$ $to$ $find$ $x:$ 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: $5^3 = 5\times5\times5 = 125$] $5^x = 5^3$ $x = 3$