Q 18. - Precalculus Enhanced with Graphing Utilities

Question

Change the given logarithmic statement to an equivalent statement involving an exponent. 

${\log }_3\left(\frac{1}{9}\right)=-2$

Step-by-Step Solution

Answer

The equivalent exponential statement of the given logarithmic statement is  $3^{-2}=\frac{1}{9}$.

Step 1. Given information

A logarithmic statement is given as ${\log }_3\left(\frac{1}{9}\right)=-2$.

Step 2. Formula Used

The logarithmic function $y={\log }_a\left(x\right)$can be changed into an exponential statement as $x=a^y$.

Step 3. Conversion

The logarithmic statement is ${\log }_3\left(\frac{1}{9}\right)=-2$.

Compare statement with $y={\log }_a\left(x\right)$.

$x=\frac{1}{9}, a=3$, and $y=-2$

So, the corresponding exponential statement is

$3^{-2}=\frac{1}{9}$