Math Problem Statement
What is the result of \( \log_4 64 \)?
Solution
The image you uploaded asks to find the value of .
To solve , we need to rewrite 64 as a power of 4.
We know:
Using the logarithmic property: We can simplify:
Thus, the result of is 3.
Would you like more details or further explanations? Here are some related questions:
- How do you simplify logarithmic expressions?
- What are the basic properties of logarithms?
- How can we change the base of a logarithm using the change-of-base formula?
- How do you solve logarithmic equations?
- 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