## Precalculus: Mathematics for Calculus, 7th Edition

a.) $x = -2$ b.) $x = 32$
$Use$ $the$ $definition$ $of$ $the$ $logarithmic$ $function$ $to$ $find$ $x:$ a.) $\log_7 (\frac{1}{49}) = x$ b.) $\log_2 x = 5$ a.) $\log_7 (\frac{1}{49}) = x$ Rewrite $\frac{1}{49}$ as $7^{-2}$ [Note: $7^{-2} = \frac{1}{ 7\times7} = \frac{1}{49}$] $$\log_7 7^{-2} = x$$ Use the Third Property of Logarithms: $\log_a a^x = x$ $$log_7 7^{-2} = x \rightarrow -2 = x$$ $$x = -2$$ b.) $\log_2 x = 5$ Rewrite the logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$ $$\log_2 x = 5 \rightarrow 2^5 = x$$ $$x = 2\times2\times2\times2\times2$$ $$x = 32$$