Evaluate log base 36 of fifth root of 6

Problem

(log_36)(√(5,6))

Solution

1. Rewrite the radical expression using a fractional exponent.

√(5,6)=6(1/5)

2. Express the base of the logarithm as a power of 6.

36=6

3. Substitute these values back into the logarithmic expression.

(log_6)(6(1/5))

4. Apply the change of base formula or the property (log_bn)(am)=m/n*(log_b)(a)

(1/5)/2*(log_6)(6)

5. Simplify the expression using the identity (log_b)(b)=1

1/5⋅1/2⋅1

6. Multiply the fractions to find the final value.

1/10

Final Answer

(log_36)(√(5,6))=1/10

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