Math Problem Statement
Solution
Let's simplify both parts of the question step by step.
(a)
First, evaluate , which means "logarithm of 3 to the base 8." There's no simple integer value for this, so we leave it as is. Now focus on the given expression:
Notice that can be simplified:
Thus, the expression becomes:
Without more simplification for , we would leave the final expression as:
(b)
To simplify this:
Using the logarithmic property , we can simplify:
Since , the expression simplifies to:
So, the answer for part (b) is .
Let me know if you need more details or have any questions! Here are five related questions you might consider:
- What is the exact value of ?
- Can we express using natural or common logarithms?
- How would the answer change if the base in part (b) was different?
- How does the property ( \log_b (a^x) = x \log_b a \
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Math Problem Analysis
Mathematical Concepts
Logarithms
Exponents
Properties of Logarithms
Formulas
log_b(a^x) = x * log_b(a)
log_b(b) = 1
Theorems
Logarithmic Exponent Rule
Logarithm Identity
Suitable Grade Level
Grades 10-12
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