What is log_{10}(x/(3y)) ?

The solution to log_{10}(x/(3y)) is log_{10}(x)-log_{10}(3)-log_{10}(y)

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simplify log_{10}(x/(3y))

simplify

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

lo g_{10} (x) - lo g_{10} (3) - lo g_{10} (y)

Solution steps

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

Apply log rule:

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

lo g_{10} (\frac{x}{3 y}) = lo g_{10} (x) - lo g_{10} (3 y)

= lo g_{10} (x) - lo g_{10} (3 y)

Simplify

lo g_{10} (3 y) : lo g_{10} (3) + lo g_{10} (y)

= lo g_{10} (x) - (lo g_{10} (3) + lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{10} (3) + lo g_{10} (y)) = - lo g_{10} (3) - lo g_{10} (y)

= lo g_{10} (x) - lo g_{10} (3) - lo g_{10} (y)

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

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

ln (3) + \frac{1}{3} ln (4 - x^{2}) - ln (x)

- lo g_{10} (5 \times 1 0^{- 3})

lo g_{10} (15) - lo g_{10} (5)

What is log_{10}(x/(3y)) ?
The solution to log_{10}(x/(3y)) is log_{10}(x)-log_{10}(3)-log_{10}(y)