Q. 15 - Precalculus Enhanced with Graphing Utilities

Question

Change the given exponential statement to an equivalent statement involving a logarithm.

$e^x=8$

Step-by-Step Solution

Answer

The equivalent logarithmic statement of the given exponential statement is $x={\log }_e\left(8\right)$

Step 1. Given information

An exponential equation is given as $e^x=8$.

Step 2. Formula

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

Step 3. Simplification

The exponential statement is $e^x=8$.

Compare statement with $x=a^y$.

$x=8, a=e$, and $y=x$

So, the corresponding logarithmic statement is

$x={\log }_e\left(8\right)$