Question

Evaluate the expression ${\log }_4\left(256\right)$.

Short answer

The simplified value of expression is $4$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is ${\log }_4\left(256\right)$.

Step 2. Simplify the expression.

The given expression ${\log }_4\left(256\right)$is evaluated as:

$\begin{array}{l}{\log }_4\left(256\right)={\log }_4{\left(4\right)}^4\\ =4{\log }_4\left(4\right)\\ =\mathrm{4....}\left({\log }_{a}a=1\right)\end{array}$

Step 3. Conclusion.

The simplified value of expression is $4$.