QuestionDecember 26, 2025

16. Expand the expression: logsqrt [6]((x)/(y))

16. Expand the expression: logsqrt [6]((x)/(y))
16. Expand the expression: logsqrt [6]((x)/(y))

Solution
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Answer

\frac{1}{6}[log(x) - log(y)] Explanation 1. Rewrite the radical as an exponent \sqrt[6]{\frac{x}{y}} = \left(\frac{x}{y}\right)^{1/6} 2. Apply logarithm power rule log\left(\frac{x}{y}\right)^{1/6} = \frac{1}{6}log\left(\frac{x}{y}\right) 3. Apply logarithm quotient rule log\left(\frac{x}{y}\right) = log(x) - log(y)

Explanation

1. Rewrite the radical as an exponent<br /> $\sqrt[6]{\frac{x}{y}} = \left(\frac{x}{y}\right)^{1/6}$<br />2. Apply logarithm power rule<br /> $log\left(\frac{x}{y}\right)^{1/6} = \frac{1}{6}log\left(\frac{x}{y}\right)$<br />3. Apply logarithm quotient rule<br /> $log\left(\frac{x}{y}\right) = log(x) - log(y)$
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