Q38. - Algebra 2

Question

Evaluate each expression.

 

${\log }_{3}243$

Step-by-Step Solution

Answer

The value of ${\log }_{3}243=5$.

Step 1. Given Information.

Given, to evaluate the expression ${\log }_{3}243$.

Step 2. Calculation .

According to the properties of logarithms, ${\log }_b{a}^n=n{\log }_{b}a,{\log }_{a}a=1$

 

Simplifying the expression:

 $\begin{array}{l}{\log }_{3}243={\log }_3{3}^5\\ {\log }_{3}243=5{\log }_{3}3\\ {\log }_{3}243=5\left(1\right)\\ {\log }_{3}243=5\end{array}$

Step 3. Conclusion .

Hence, ${\log }_{3}243=5$.