What is expand log_{9}(sqrt((\sqrt{9x^7))/y}) ?

The solution to expand log_{9}(sqrt((\sqrt{9x^7))/y}) is 1/2 log_{9}((3x^3sqrt(x))/y)

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expand log_{9}(sqrt((\sqrt{9x^7))/y})

expand

lo g_{9} \frac{9 x ^{7}}{y}

\frac{1}{2} lo g_{9} (\frac{3 x ^{3} x}{y})

Solution steps

lo g_{9} \frac{9 x ^{7}}{y}

\frac{9 x ^{7}}{y} = \frac{3 x ^{3} x}{y}

= lo g_{9} \frac{3 x ^{3} x}{y}

Rewrite as

= lo g_{9} ((\frac{3 x ^{3} x}{y})^{\frac{1}{2}})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= \frac{1}{2} lo g_{9} (\frac{3 x ^{3} x}{y})

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\frac{1}{x ^{2} ( x + 2 )}

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What is expand log_{9}(sqrt((\sqrt{9x^7))/y}) ?
The solution to expand log_{9}(sqrt((\sqrt{9x^7))/y}) is 1/2 log_{9}((3x^3sqrt(x))/y)