Q 19. - Precalculus Enhanced with Graphing Utilities

Question

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

${\log }_a\left(3\right)=6$

Step-by-Step Solution

Answer

The equivalent exponential statement of the given logarithmic statement is  $a^6=3$

Step 1. Given information

A logarithmic statement is given as ${\log }_a\left(3\right)=6$.

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 ${\log }_a\left(3\right)=6$.

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

$x=3, a=a$, and $y=6$

So, the corresponding exponential statement is

$a^6=3$