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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

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

ln (\frac{x y}{x})

3 ln (\frac{x}{x + 1})

lo g_{10} (e^{- x} cos (π x))

2 - 2 ln (2) + 2 ln (x)

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