Q 105. - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation. 

${\log }_2{8}^x=-3$

Step-by-Step Solution

Answer

The solution to the equation, ${\log }_2{8}^x=-3$is, $x=-1$.

Step 1. Given Information

The given equation to be solved is ${\log }_2{8}^x=-3$.

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 ${\log }_2{8}^x=-3$.

Use rule of change from logarithm to exponents: 

$$\begin{gathered} {\log }_2{8}^x=-3 \\ {2}^{-3}=8^x \\ {\left(2^3\right)}^x=\left(2{)}^{-3} \\ \right(2{)}^{3x}=(2{)}^{-3} \\ 3x=-3 \\ x=-1 \end{gathered}$$

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