What is 3log_{2}(x)-4log_{2}(y)+1/2 log_{2}(z) ?

The solution to 3log_{2}(x)-4log_{2}(y)+1/2 log_{2}(z) is log_{2}((x^3}{y^4})+\frac{log_{2}(z))/2

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simplify 3log_{2}(x)-4log_{2}(y)+1/2 log_{2}(z)

simplify

3 lo g_{2} (x) - 4 lo g_{2} (y) + \frac{1}{2} lo g_{2} (z)

lo g_{2} (\frac{x ^{3}}{y ^{4}}) + \frac{lo g _{2} ( z )}{2}

Solution steps

3 lo g_{2} (x) - 4 lo g_{2} (y) + \frac{1}{2} lo g_{2} (z)

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

- 4 lo g_{2} (y) = - lo g_{2} (y^{4})

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

= lo g_{2} (x^{3}) - lo g_{2} (y^{4}) + 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^{4}) = lo g_{2} (\frac{x ^{3}}{y ^{4}})

= lo g_{2} (\frac{x ^{3}}{y ^{4}}) + 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 ^{4}}) + \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 ^{4}}) + \frac{lo g _{2} ( z )}{2}

ln (2 (7) + 1) + 2 ln ((7) - 1)

lo g_{10} (x^{3} + 3 x^{2} - 4 x) - lo g_{10} (x^{2} - 2 x + 1)

1.344 \cdot ln (\frac{495}{639})

\frac{2}{7} lo g_{10} (a) - \frac{1}{4} lo g_{10} (b)

- lo g_{10} (2.68 \cdot 1 0^{- 3})

What is 3log_{2}(x)-4log_{2}(y)+1/2 log_{2}(z) ?
The solution to 3log_{2}(x)-4log_{2}(y)+1/2 log_{2}(z) is log_{2}((x^3}{y^4})+\frac{log_{2}(z))/2