Math Problem Statement
Solution
The problem asks to evaluate .
Solution:
The logarithmic equation can be rewritten as:
Now express 32 as a power of 4. We know that , and . Thus: and
Equating the exponents:
Solve for :
Thus:
Final Answer:
Would you like further explanation on logarithms or properties of exponents?
Here are some related questions for practice:
- Evaluate .
- Simplify .
- Solve .
- Convert to exponential form.
- What is the value of ?
Tip: When solving logarithms, always check if the argument (e.g., 32 in this case) can be expressed as a power of the base.
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Math Problem Analysis
Mathematical Concepts
Logarithms
Exponents
Equation Solving
Formulas
log_b(a) = x implies b^x = a
a^(mn) = (a^m)^n
Theorems
Properties of Logarithms
Exponentiation Rules
Suitable Grade Level
Grades 9-12
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