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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

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

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

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

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

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

lo g_{x} (\frac{2}{3})

lo g_{10} (\frac{\frac{1}{9}}{k})

ln (x y) + 9 ln (\frac{y}{z}) - 8 ln (x yz)

5 lo g_{10} (y) - 3 lo g_{10} (m)

5 lo g_{6} (u) + 8 lo g_{6} (v)

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