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

The solution to log_{2}(3/(2x)) is log_{2}(3)-1-log_{2}(x)

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

simplify

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

lo g_{2} (3) - 1 - lo g_{2} (x)

Solution steps

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

Apply log rule:

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

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

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

Simplify

lo g_{2} (2 x) : 1 + lo g_{2} (x)

= lo g_{2} (3) - (1 + lo g_{2} (x))

Apply the distributive law:

- (a + b) = - a - b

- (1 + lo g_{2} (x)) = - 1 - lo g_{2} (x)

= lo g_{2} (3) - 1 - lo g_{2} (x)

lo g_{a} (\frac{x ^{4}}{y ^{2} a ^{7}})

ln (\frac{e ^{6}}{10})

lo g_{3} (6) + 2 lo g_{3} (x) + \frac{1}{2} lo g_{3} (9)

lo g_{10} (x) + lo g_{10} (y) + lo g_{10} (2 z)

lo g_{10} (\frac{x}{100 y ^{4}})

What is log_{2}(3/(2x)) ?
The solution to log_{2}(3/(2x)) is log_{2}(3)-1-log_{2}(x)