What is log_{10}((3x)/(2y)) ?

The solution to log_{10}((3x)/(2y)) is log_{10}(3)+log_{10}(x)-log_{10}(2)-log_{10}(y)

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simplify log_{10}((3x)/(2y))

simplify

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

lo g_{10} (3) + lo g_{10} (x) - lo g_{10} (2) - lo g_{10} (y)

Solution steps

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

Apply log rule:

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

lo g_{10} (\frac{3 x}{2 y}) = lo g_{10} (3 x) - lo g_{10} (2 y)

= lo g_{10} (3 x) - lo g_{10} (2 y)

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

lo g_{10} (2 y) = lo g_{10} (2) + lo g_{10} (y)

= lo g_{10} (3) + lo g_{10} (x) - (lo g_{10} (2) + lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{10} (2) + lo g_{10} (y)) = - lo g_{10} (2) - lo g_{10} (y)

= lo g_{10} (3) + lo g_{10} (x) - lo g_{10} (2) - lo g_{10} (y)

ln (\frac{1}{4 9 ^{k}})

ln (\frac{1}{2 5 ^{k}})

lo g_{10} (x + 2) + lo g_{10} (x - 2)

2 ln (x) - ln (y)

ln (x) + ln (15)

What is log_{10}((3x)/(2y)) ?
The solution to log_{10}((3x)/(2y)) is log_{10}(3)+log_{10}(x)-log_{10}(2)-log_{10}(y)