What is expand log_{9}(sqrt((z^5)/(xm^5))) ?

The solution to expand log_{9}(sqrt((z^5)/(xm^5))) is 1/2 (5log_{9}(z)-log_{9}(xm^5))

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expand log_{9}(sqrt((z^5)/(xm^5)))

expand

lo g_{9} (\frac{z ^{5}}{x m ^{5}})

\frac{1}{2} (5 lo g_{9} (z) - lo g_{9} (x m^{5}))

Solution steps

lo g_{9} (\frac{z ^{5}}{x m ^{5}})

Rewrite as

= lo g_{9} ((\frac{z ^{5}}{x m ^{5}})^{\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{z ^{5}}{x m ^{5}})

Simplify

lo g_{9} (\frac{z ^{5}}{x m ^{5}}) : 5 lo g_{9} (z) - lo g_{9} (x m^{5})

= \frac{1}{2} (5 lo g_{9} (z) - lo g_{9} (x m^{5}))

lo g_{9} (x m^{5}) = lo g_{9} (x) + 5 lo g_{9} (m)

= \frac{1}{2} (5 lo g_{9} (z) - (lo g_{9} (x) + 5 lo g_{9} (m)))

lo g_{9} (x) + 5 lo g_{9} (m) = lo g_{9} (x m^{5})

= \frac{1}{2} (5 lo g_{9} (z) - lo g_{9} (x m^{5}))

lo g_{9} (x m^{5}) = lo g_{9} (x) + 5 lo g_{9} (m)

= \frac{1}{2} (5 lo g_{9} (z) - (lo g_{9} (x) + 5 lo g_{9} (m)))

lo g_{9} (x) + 5 lo g_{9} (m) = lo g_{9} (x m^{5})

= \frac{1}{2} (5 lo g_{9} (z) - lo g_{9} (x m^{5}))

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What is expand log_{9}(sqrt((z^5)/(xm^5))) ?
The solution to expand log_{9}(sqrt((z^5)/(xm^5))) is 1/2 (5log_{9}(z)-log_{9}(xm^5))