Question

Evaluate each expression.

${\log }_{2}128$

Short answer

The value of ${\log }_{2}128=7$.

Step-by-step solution

Step 1. Given Information.

Given, to evaluate the expression ${\log }_{2}128$.

Step 2. Calculation.

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

Simplifying the expression:

$\begin{array}{l}{\log }_{2}128={\log }_2{2}^7\\ {\log }_{2}128=7{\log }_{2}2\\ {\log }_{2}128=7\left(1\right)\\ {\log }_{2}128=7\end{array}$

Step 3. Conclusion.

Hence, ${\log }_{2}128=7$.