Evaluate log of 5 cube root of 25

Problem

(log_5)(√(3,25))

Solution

1. Rewrite the expression using standard logarithmic notation, assuming base 5 based on the phrasing "log of 5".

(log_5)(√(3,25))

2. Express the radicand as a power of 5.

25=5

3. Convert the cube root into a fractional exponent.

√(3,5)=5

4. Substitute the exponential form back into the logarithm.

(log_5)(5)

5. Apply the power rule for logarithms, (log_b)(bx)=x

(log_5)(5)=2/3

Final Answer

(log_5)(√(3,25))=2/3

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