Question

Evaluate each expression.

${\log }_{3}243$

Short answer

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

Step-by-step solution

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