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

The solution to log_{a}(3/(2x)) is log_{a}(3)-log_{a}(2)-log_{a}(x)

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simplify log_{a}(3/(2x))

simplify

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

lo g_{a} (3) - lo g_{a} (2) - lo g_{a} (x)

Solution steps

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

Apply log rule:

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

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

= lo g_{a} (3) - lo g_{a} (2 x)

Simplify

lo g_{a} (2 x) : lo g_{a} (2) + lo g_{a} (x)

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

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{a} (2) + lo g_{a} (x)) = - lo g_{a} (2) - lo g_{a} (x)

= lo g_{a} (3) - lo g_{a} (2) - lo g_{a} (x)

ln (x) - 3 [ln (x - 2) + ln (x + 2)]

14 lo g_{10} (8) (x + 5) - 9 lo g_{10} (8 y)

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

lo g_{10} (\frac{x ^{4}}{y ^{5}})

lo g_{4} (\frac{16}{x + 6})

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