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Chapter 12: Q37. (page 637)

Evaluate each expression.
$\log_{2} 128$

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given Information.

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

02

Step 2. Calculation.

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

Simplifying the expression:

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

03

Step 3. Conclusion.

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

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