Expand the Logarithmic Expression log of fourth root of x/y

Problem

(log_)(√(4,x/y))

Solution

1. Rewrite the radical expression using a fractional exponent.

(log_)(x/y)

2. Apply the power rule for logarithms, (log_b)(ap)=p*(log_b)(a) to move the exponent to the front.

1/4*(log_)(x/y)

3. Apply the quotient rule for logarithms, (log_b)(a/c)=(log_b)(a)−(log_b)(c) to expand the term inside the parentheses.

1/4*((log_)(x)−(log_)(y))

4. Distribute the fraction to each term to reach the final expanded form.

1/4*(log_)(x)−1/4*(log_)(y)

Final Answer

(log_)(√(4,x/y))=1/4*(log_)(x)−1/4*(log_)(y)

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