Q 97. - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation. 

${\log }_{3}243=2x+1$

Step-by-Step Solution

Answer

The solution to the equation, ${\log }_{3}243=2x+1$is, $x=2$.

Step 1. Given Information

The given equation to be solved is ${\log }_{3}243=2x+1$.

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 ${\log }_{3}243=2x+1$.

Use rule of change from logarithm to exponents: 

$$\begin{gathered} {\log }_{3}243=2x+1 \\ {3}^{2x+1}=243 \\ (3{)}^{2x+1}=(3{)}^5 \\ 2 x+1=5 \\ 2x=5 \\ x=2 \end{gathered}$$

The solution to the given equation is, $x=2$.