To find \(\log_2 64\), you need to determine the exponent to which 2 must be raised to obtain 64.

We can express 64 as a power of 2:

\[
64 = 2^6
\]

Thus,

\[
\log_2 64 = \log_2 (2^6)
\]

Using the logarithm power rule \(\log_b (a^c) = c \cdot \log_b a\), where \(b\) is the base of the logarithm and \(a\) is the argument:

\[
\log_2 (2^6) = 6 \cdot \log_2 (2)
\]

Since \(\log_2 2 = 1\), this simplifies to:

\[
\log_2 64 = 6
\]

So, \(\log_2 64 = 6\).

### Do you want more details or have any questions?

Here are some related questions you might find interesting:

1. What is \(\log_2 32\)?
2. How do you calculate \(\log_3 81\)?
3. What are the general properties of logarithms?
4. How do you solve logarithmic equations like \(\log_5(x) = 3\)?
5. What is the change of base formula for logarithms?

**Tip:** Remember, logarithms are the inverse operations of exponentiation, meaning they help us find the power to which a base must be raised to produce a given number.

Discover how to calculate \(\log_2 64\) using the logarithm power rule. This detailed guide explains how to determine the exponent needed to raise 2 to obtain 64. Suitable for high school students and anyone interested in logarithmic calculations.

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