Math Problem Statement

What is the result of \( \log_4 64 \)?

Solution

The image you uploaded asks to find the value of log464\log_4 64.

To solve log464\log_4 64, we need to rewrite 64 as a power of 4.

We know: 64=4364 = 4^3

Using the logarithmic property: logbbx=x\log_b b^x = x We can simplify: log464=log443=3\log_4 64 = \log_4 4^3 = 3

Thus, the result of log464\log_4 64 is 3.

Would you like more details or further explanations? Here are some related questions:

  1. How do you simplify logarithmic expressions?
  2. What are the basic properties of logarithms?
  3. How can we change the base of a logarithm using the change-of-base formula?
  4. How do you solve logarithmic equations?
  5. What are the differences between common and natural logarithms?

Tip: Always check if you can express the number inside a logarithm as a power of the base. This simplifies many calculations!

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponents
Algebra

Formulas

\( \log_b b^x = x \)

Theorems

Logarithmic properties

Suitable Grade Level

Grades 8-10