Q. 16 - Precalculus Enhanced with Graphing Utilities

Question

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

$e^{2.2}=M$

Step-by-Step Solution

Answer

The equivalent logarithmic statement of the given exponential statement is $2.2={\log }_e\left(M\right)$.

Step 1. Given information

An exponential equation is given as $e^{2.2}=M$

Step 2. Formula

The exponential statement $e^{2.2}=M$can be changed into a logarithmic function as $y={\log }_a\left(x\right)$.

Step 3. Simplification

The exponential statement is $e^{2.2}=M$Compare statement with $a^y=x$

$x=M,a=e$, and $y=2.2$

So, the corresponding logarithmic statement is

$2.2={\log }_e\left(M\right)$