What is expand log_{b}((x^2y)/(z^9)) ?

The solution to expand log_{b}((x^2y)/(z^9)) is 2log_{b}(x)+log_{b}(y)-9log_{b}(z)

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expand log_{b}((x^2y)/(z^9))

expand

lo g_{b} (\frac{x ^{2} y}{z ^{9}})

2 lo g_{b} (x) + lo g_{b} (y) - 9 lo g_{b} (z)

Solution steps

lo g_{b} (\frac{x ^{2} y}{z ^{9}})

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 ^{9}}) = lo g_{b} (x^{2} y) - lo g_{b} (z^{9})

= lo g_{b} (x^{2} y) - lo g_{b} (z^{9})

Apply log rule:

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

lo g_{b} (z^{9}) = 9 lo g_{b} (z)

= lo g_{b} (x^{2} y) - 9 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) - 9 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) - 9 lo g_{b} (z)

lo g_{b} (2 y + 5) - \frac{1}{2} lo g_{b} (y + 3)

4 ln (x) - \frac{1}{3} ln (y)

3 lo g_{4} ((x y)^{3}) - lo g_{4} (x y)

\frac{1}{2} lo g_{10} (a) + 7 lo g_{10} (b)

What is expand log_{b}((x^2y)/(z^9)) ?
The solution to expand log_{b}((x^2y)/(z^9)) is 2log_{b}(x)+log_{b}(y)-9log_{b}(z)