What is 3log_{2}(x)-2log_{2}(y)+1/2 log_{2}(z) ?

The solution to 3log_{2}(x)-2log_{2}(y)+1/2 log_{2}(z) is log_{2}((x^3}{y^2})+\frac{log_{2}(z))/2

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simplify 3log_{2}(x)-2log_{2}(y)+1/2 log_{2}(z)

simplify

3 lo g_{2} (x) - 2 lo g_{2} (y) + \frac{1}{2} lo g_{2} (z)

lo g_{2} (\frac{x ^{3}}{y ^{2}}) + \frac{lo g _{2} ( z )}{2}

Solution steps

3 lo g_{2} (x) - 2 lo g_{2} (y) + \frac{1}{2} lo g_{2} (z)

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

- 2 lo g_{2} (y) = - lo g_{2} (y^{2})

\frac{1}{2} lo g_{2} (z) = lo g_{2} (z^{\frac{1}{2}})

= lo g_{2} (x^{3}) - lo g_{2} (y^{2}) + lo g_{2} (z^{\frac{1}{2}})

Apply log rule:

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

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

= lo g_{2} (\frac{x ^{3}}{y ^{2}}) + lo g_{2} (z^{\frac{1}{2}})

Simplify

lo g_{2} (z^{\frac{1}{2}}) : \frac{1}{2} lo g_{2} (z)

= lo g_{2} (\frac{x ^{3}}{y ^{2}}) + \frac{1}{2} lo g_{2} (z)

Simplify

\frac{1}{2} lo g_{2} (z) : \frac{lo g _{2} ( z )}{2}

= lo g_{2} (\frac{x ^{3}}{y ^{2}}) + \frac{lo g _{2} ( z )}{2}

ln (12) - ln (25)

lo g_{e} (2 e^{+ e})

ln ((y - 1) e^{y})

ln (e^{x} \cdot 6 x)

- lo g_{10} (6.33 \cdot 1 0^{- 5})

What is 3log_{2}(x)-2log_{2}(y)+1/2 log_{2}(z) ?
The solution to 3log_{2}(x)-2log_{2}(y)+1/2 log_{2}(z) is log_{2}((x^3}{y^2})+\frac{log_{2}(z))/2