Expand the Logarithmic Expression log base 6 of fourth root of 17

Problem

(log_6)(√(4,17))

Solution

1. Rewrite the radical expression using a fractional exponent. The fourth root of a number is equivalent to raising that number to the power of 1/4

√(4,17)=17

2. Apply the power rule for logarithms, which states that (log_b)(xp)=p*(log_b)(x)

(log_6)(17)=1/4*(log_6)(17)

Final Answer

(log_6)(√(4,17))=1/4*(log_6)(17)

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