Expand the Logarithmic Expression log base 6 of cube root of 6

Problem

(log_6)(√(3,6))

Solution

1. Rewrite the radical expression using a fractional exponent.

√(3,6)=6^(1/3)

2. Apply the power rule for logarithms, which states (log_b)(x^n)=n*(log_b)(x)

(log_6)(6^(1/3))=1/3*(log_6)(6)

3. Evaluate the logarithm using the property (log_b)(b)=1

(log_6)(6)=1

4. Multiply the resulting values to find the final simplified form.

1/3⋅1=1/3

Final Answer

(log_6)(√(3,6))=1/3

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