Q. 11 - Precalculus Enhanced with Graphing Utilities

Question

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

$1.6=a^2$

Step-by-Step Solution

Answer

The equivalent logarithmic statement of the given exponential statement is  $2={\log }_a(1.6)$

Step 1. Given information

An exponential equation is given as $1.6=a^2$.

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 $1.6=a^2$.

Compare statement with $x=a^y$.

$x=1.6, a=a$, and $y=2$

So, the corresponding logarithmic statement is

$2={\log }_a(1.6)$