Q. 12 - Precalculus Enhanced with Graphing Utilities

Question

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

$2.1=a^3$

Step-by-Step Solution

Answer

The equivalent logarithmic statement of the given exponential statement is $3={\log }_a(2.1)$

Step 1. Given information

An exponential equation is given as $2.1=a^3$.

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 $2.1=a^3$.

Compare statement with $x=a^y$.

$x=2.1, a=a$, and $y=3$

So, the corresponding logarithmic statement is

$3={\log }_a(2.1)$