What is expand log_{b}((x^2y)/(z^5)) ?

The solution to expand log_{b}((x^2y)/(z^5)) is 2log_{b}(x)+log_{b}(y)-5log_{b}(z)

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expand log_{b}((x^2y)/(z^5))

expand

lo g_{b} (\frac{x ^{2} y}{z ^{5}})

2 lo g_{b} (x) + lo g_{b} (y) - 5 lo g_{b} (z)

Solution steps

lo g_{b} (\frac{x ^{2} y}{z ^{5}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{b} (\frac{x ^{2} y}{z ^{5}}) = lo g_{b} (x^{2} y) - lo g_{b} (z^{5})

= lo g_{b} (x^{2} y) - lo g_{b} (z^{5})

Apply log rule:

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

lo g_{b} (z^{5}) = 5 lo g_{b} (z)

= lo g_{b} (x^{2} y) - 5 lo g_{b} (z)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{b} (x^{2} y) = lo g_{b} (x^{2}) + lo g_{b} (y)

= lo g_{b} (x^{2}) + lo g_{b} (y) - 5 lo g_{b} (z)

Apply log rule:

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

lo g_{b} (x^{2}) = 2 lo g_{b} (x)

= 2 lo g_{b} (x) + lo g_{b} (y) - 5 lo g_{b} (z)

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What is expand log_{b}((x^2y)/(z^5)) ?
The solution to expand log_{b}((x^2y)/(z^5)) is 2log_{b}(x)+log_{b}(y)-5log_{b}(z)