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Chapter 3: Problem 9

Evaluate the indicated expression. Do not use a calculator for these exercises. $$ \log _{2} 64 $$

Short Answer

Expert verified
The expression \(\log_{2}{64}\) can be written in the exponential form as \(2^x = 64\). To find the exponent x, we need to find the power to which 2 must be raised to obtain 64. Since \(2^6 = 64\), we can conclude that x = 6. Thus, \(\log_{2}{64} = 6\).

Step by step solution

01

Understand the logarithm expression

We need to evaluate the expression \(\log_{2}{64}\). This can be written in the exponential form as \(2^x = 64\), where x is the exponent we need to find.
02

Convert the expression into exponential form

We can convert the logarithm expression \(\log_{2}{64}\) into the exponential form as \(2^x = 64\).
03

Find the exponent

To find the exponent x, we need to find the power to which 2 must be raised to obtain 64. Since \(2^6 = 64\), we can conclude that x = 6.
04

Write the answer

The exponent x that satisfies the expression \(2^x = 64\) is 6. Therefore, \(\log_{2}{64} = 6\).

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