What is expand log_{b}((x^2y)/(z^3)) ?

The solution to expand log_{b}((x^2y)/(z^3)) is 2log_{b}(x)+log_{b}(y)-3log_{b}(z)

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expand log_{b}((x^2y)/(z^3))

expand

lo g_{b} (\frac{x ^{2} y}{z ^{3}})

2 lo g_{b} (x) + lo g_{b} (y) - 3 lo g_{b} (z)

Solution steps

lo g_{b} (\frac{x ^{2} y}{z ^{3}})

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 ^{3}}) = lo g_{b} (x^{2} y) - lo g_{b} (z^{3})

= lo g_{b} (x^{2} y) - lo g_{b} (z^{3})

Apply log rule:

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

lo g_{b} (z^{3}) = 3 lo g_{b} (z)

= lo g_{b} (x^{2} y) - 3 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) - 3 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) - 3 lo g_{b} (z)

ln (\frac{21}{31})

32 \cdot ln (6 x)

lo g_{8} (a^{3} b^{4})

- lo g_{10} (1.1 \cdot 1 0^{- 2})

lo g_{e} (\frac{e}{2})

What is expand log_{b}((x^2y)/(z^3)) ?
The solution to expand log_{b}((x^2y)/(z^3)) is 2log_{b}(x)+log_{b}(y)-3log_{b}(z)