Question

question 6 of 10
evaluate the following expression. you should do this problem without a calculator.
\\(\log_2 32\\)
a. 5
b. 6
c. 8
d. 16

Explanation:

Step1: Recall the logarithm definition

The logarithm \(\log_{b}a = x\) is equivalent to \(b^{x}=a\). For \(\log_{2}32\), we need to find \(x\) such that \(2^{x}=32\).

Step2: Express 32 as a power of 2

We know that \(2^{5}=32\) (since \(2\times2\times2\times2\times2 = 32\)).

Step3: Compare with the logarithm definition

From \(2^{x}=32\) and \(2^{5}=32\), we can see that \(x = 5\). So \(\log_{2}32=5\).

Answer:

A. 5