Q37.

Evaluate each expression.

$\log_{2} 128$

Verified

Answer

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

1Step 1. Given Information.

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

2Step 2. Calculation .

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

Simplifying the expression:

$\begin{array}{l} \log_{2} 128 = \log_{2} 2^{7} \\ \log_{2} 128 = 7 \log_{2} 2 \\ \log_{2} 128 = 7 (1) \\ \log_{2} 128 = 7 \end{array}$

3Step 3. Conclusion .

Hence, $\log_{2} 128 = 7$ .