Q 106. - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation.

Step-by-Step Solution

Answer

The solution to the equation,

${\log }_3{3}^x=-1$

Step 1. Given Information

The given equation to be solved is ${\log }_3{3}^x=-1$is, $x=-1$.

Step 2. Formula used

Rule of change from logarithm to exponents: 

${\log }_{a}b=y\Rightarrow a^y=b$

Step 3. Finding Solution

The given equation is ${\log }_3{3}^x=-1$.

Use rule of change from logarithm to exponents: 

$$\begin{gathered} {\log }_3{3}^x=-1 \\ {3}^{-1}=3^x \\ {\left(3\right)}^x={\left(3\right)}^{-1}x=-1 \end{gathered}$$

The solution to the given equation is,  $x=-1$.