What is log_{b}(x/(yz)) ?

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

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simplify log_{b}(x/(yz))

simplify

lo g_{b} (\frac{x}{yz})

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

Solution steps

lo g_{b} (\frac{x}{yz})

Apply log rule:

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

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

= lo g_{b} (x) - lo g_{b} (yz)

Simplify

lo g_{b} (yz) : lo g_{b} (y) + lo g_{b} (z)

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

Apply the distributive law:

- (a + b) = - a - b

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

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

\frac{1}{2} ln (x) + ln (y)

\frac{2}{5} ln (\frac{15}{2})

lo g_{10} (\frac{z ^{5}}{x ^{3} y})

\frac{1}{2} lo g_{10} (x) + 3 lo g_{10} (x + 1)

lo g_{10} (6) - lo g_{10} (2)

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