Evaluate log base 8 of 1/( square root of 8)

Problem

(log_8)(1/√(,8))

Solution

1. Rewrite the square root using a fractional exponent.

√(,8)=8(1/2)

2. Express the fraction as a power with a negative exponent.

1/(8(1/2))=8(−1/2)

3. Substitute this expression back into the logarithm.

(log_8)(8(−1/2))

4. Apply the logarithm power rule (log_b)(bx)=x

(log_8)(8(−1/2))=−1/2

Final Answer

(log_8)(1/√(,8))=−1/2

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