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Question

Difficulty: EasyLogarithms and Change of Base

What is the value of log⁡481log⁡43\frac{\log_4 81}{\log_4 3}?

Answer: 4

Answer

4
Applying the change of base property log⁡cblog⁡ca=log⁡ab\frac{\log_c b}{\log_c a} = \log_a b, the ratio log⁡481log⁡43\frac{\log_4 81}{\log_4 3} reduces directly to log⁡381\log_3 81. Since 34=813^4 = 81, the value is 4.

Step-by-Step Solution

1
Apply the change of base formula to rewrite the ratio
\frac{\log_4 81}{\log_4 3} = \log_3 81
By the change of base identity, log⁡cblog⁡ca=log⁡ab\frac{\log_c b}{\log_c a} = \log_a b.
2
Evaluate the logarithm
4
Since 34=813^4 = 81, log⁡381=4\log_3 81 = 4.

Key Concept

Change of Base Formula for Logarithms
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Topics

Logarithms and Change of Base

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