Q. 14 - Precalculus Enhanced with Graphing Utilities

Question

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

$3^x=4.6$

Step-by-Step Solution

Answer

The equivalent logarithmic statement of the given exponential statement is  $x={\log }_3(4.6)$

Step 1. Given information

An exponential equation is given as $3^x=4.6$

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 $4.6=3^x$.

Compare statement with $x=a^y$.

$x=4.6, a=3$, and $y=x$

So, the corresponding logarithmic statement is

$x={\log }_3(4.6)$