What is 2log_{2}(3x)-3log_{2}(5x) ?

The solution to 2log_{2}(3x)-3log_{2}(5x) is log_{2}(9/(125x))

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simplify 2log_{2}(3x)-3log_{2}(5x)

simplify

2 lo g_{2} (3 x) - 3 lo g_{2} (5 x)

lo g_{2} (\frac{9}{125 x})

Solution steps

2 lo g_{2} (3 x) - 3 lo g_{2} (5 x)

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

- 3 lo g_{2} (5 x) = - lo g_{2} ((5 x)^{3})

= lo g_{2} ((3 x)^{2}) - lo g_{2} ((5 x)^{3})

Apply log rule:

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

lo g_{2} ((3 x)^{2}) - lo g_{2} ((5 x)^{3}) = lo g_{2} (\frac{( 3 x ) ^{2}}{( 5 x ) ^{3}})

= lo g_{2} (\frac{( 3 x ) ^{2}}{( 5 x ) ^{3}})

Simplify

\frac{( 3 x ) ^{2}}{( 5 x ) ^{3}} : \frac{9}{125 x}

= lo g_{2} (\frac{9}{125 x})

\frac{1}{3} (ln (64) - ln (8 x^{3}))

lo g_{x} (22)

lo g_{b} (y z^{6})

lo g_{10} (\frac{R ^{5} S ^{4}}{Z ^{6}})

What is 2log_{2}(3x)-3log_{2}(5x) ?
The solution to 2log_{2}(3x)-3log_{2}(5x) is log_{2}(9/(125x))