Evaluate log base 8 of square root of 8

Problem

(log_8)(√(,8))

Solution

1. Identify the expression as a logarithm with base 8 and an argument of √(,8)

2. Rewrite the square root using a fractional exponent.

√(,8)=8(1/2)

3. Substitute the exponential form back into the logarithmic expression.

(log_8)(8(1/2))

4. Apply the property of logarithms that states (log_b)(bx)=x

(log_8)(8(1/2))=1/2

Final Answer

(log_8)(√(,8))=1/2

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