Simplify/Condense -1/3* log of 8

Problem

−1/3*(log_)(8)

Solution

1. Identify the logarithmic power rule, which states that n*(log_)(b)=(log_)(bn)

2. Apply the rule by moving the coefficient −1/3 to the exponent of the argument.

(log_)(8(−1/3))

3. Rewrite the negative exponent as a reciprocal.

(log_)(1/8)

4. Evaluate the cube root of 8, since 8=√(3,8)=2

(log_)(1/2)

Final Answer

−1/3*(log_)(8)=(log_)(1/2)

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