Q 20. - Precalculus Enhanced with Graphing Utilities

Question

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

${\log }_b\left(4\right)=2$

Step-by-Step Solution

Answer

The equivalent exponential statement of the given logarithmic statement is $b^2=4$.

Step 1. Given information

A logarithmic statement is given as ${\log }_b\left(4\right)=2$.

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 ${\log }_b\left(4\right)=2$.

Compare statement with y=log(x).

$x=4, a=b$, and $y=2$

So, the corresponding exponential statement is

$b^2=4$