What is log_{b}(x)+2log_{b}(y)-3log_{b}(z) ?

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

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simplify log_{b}(x)+2log_{b}(y)-3log_{b}(z)

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

lo g_{5} ((x - 1)^{2}) (4 x)

lo g_{10} (\frac{s}{t})

ln (\frac{4 w}{7})

ln (x) + ln (1 - x)

lo g_{10} (z) + lo g_{10} (11 y)

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