Evaluate log base 4 of 8

Problem

(log_4)(8)

Solution

1. Identify the expression as a logarithm with base 4 and argument 8.

2. Apply the change of base formula to rewrite the expression using a common base, such as base 2.

(log_4)(8)=(log_2)(8)/(log_2)(4)

3. Evaluate the numerator by expressing 8 as a power of 2, where 2=8

(log_2)(8)=3

4. Evaluate the denominator by expressing 4 as a power of 2, where 2=4

(log_2)(4)=2

5. Simplify the resulting fraction.

3/2=1.5

Final Answer

(log_4)(8)=3/2

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