Question

Evaluate the expression ${\log }_2\left(\frac{1}{8}\right)$.

Short answer

The simplified value of expression is $-3$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is ${\log }_2\left(\frac{1}{8}\right)$.

Step 2. Simplify the expression.

The given expression ${\log }_2\left(\frac{1}{8}\right)$is evaluated as:

$\begin{array}{l}{\log }_2\left(\frac{1}{8}\right)={\log }_2\left(1\right)-{\log }_2\left(8\right)\\ =0-{\log }_2{\left(2\right)}^3\\ =0-3{\log }_2\left(2\right)\\ =-\mathrm{3....}\left({\log }_{a}a=1\right)\end{array}$

Step 3. Conclusion.

The simplified value of expression is $-3$.