What is 2log_{2}(x)-4log_{2}(y)-5log_{2}(z) ?

The solution to 2log_{2}(x)-4log_{2}(y)-5log_{2}(z) is log_{2}((x^2)/(y^4z^5))

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simplify 2log_{2}(x)-4log_{2}(y)-5log_{2}(z)

simplify

2 lo g_{2} (x) - 4 lo g_{2} (y) - 5 lo g_{2} (z)

lo g_{2} (\frac{x ^{2}}{y ^{4} z ^{5}})

Solution steps

2 lo g_{2} (x) - 4 lo g_{2} (y) - 5 lo g_{2} (z)

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

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

- 5 lo g_{2} (z) = - lo g_{2} (z^{5})

= lo g_{2} (x^{2}) - lo g_{2} (y^{4}) - lo g_{2} (z^{5})

Apply log rule:

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

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

= lo g_{2} (\frac{x ^{2}}{y ^{4}}) - lo g_{2} (z^{5})

Apply log rule:

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

lo g_{2} (\frac{x ^{2}}{y ^{4}}) - lo g_{2} (z^{5}) = lo g_{2} (\frac{\frac{x ^{2}}{y ^{4}}}{z ^{5}})

= lo g_{2} (\frac{\frac{x ^{2}}{y ^{4}}}{z ^{5}})

Simplify

\frac{\frac{x ^{2}}{y ^{4}}}{z ^{5}} : \frac{x ^{2}}{y ^{4} z ^{5}}

= lo g_{2} (\frac{x ^{2}}{y ^{4} z ^{5}})

lo g_{10} (\frac{x ^{2} + 9}{x + 1})

ln (\frac{1}{0.32})

lo g_{4} (\frac{f}{16})

9 ln (x) - \frac{1}{7} ln (y)

4 lo g_{2} (u) + 5 lo g_{2} (v)

What is 2log_{2}(x)-4log_{2}(y)-5log_{2}(z) ?
The solution to 2log_{2}(x)-4log_{2}(y)-5log_{2}(z) is log_{2}((x^2)/(y^4z^5))