Problem 23
Question
Evaluate each expression without using a calculator. $$\log _{2} 64$$
Step-by-Step Solution
Verified Answer
6
1Step 1: Understand the logarithmic expression
The expression given is \( \log _{2} 64 \). In this logarithm \( \log _{2} X \), the base is 2 and the number is 64. It is read as: what power should 2 be raised to obtain 64?
2Step 2: Evaluate the logarithmic expression
We need to find the power, let’s say 'p', such that \( 2^p = 64 \). From our knowledge of powers of 2, we know that \( 2^6 = 64 \). Therefore, p equals 6 in this case. Hence, \( \log _{2} 64 = 6 \).
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