What is 5log_{2}(x)+3/4 log_{2}(y)-log_{2}(z) ?

The solution to 5log_{2}(x)+3/4 log_{2}(y)-log_{2}(z) is log_{2}((x^5\sqrt[4]{y^3})/z)

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simplify 5log_{2}(x)+3/4 log_{2}(y)-log_{2}(z)

simplify

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

Solution steps

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

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

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

= lo g_{2} (x^{5}) + lo g_{2} (y^{\frac{3}{4}}) - lo g_{2} (z)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{2} (x^{5}) + lo g_{2} (y^{\frac{3}{4}}) = lo g_{2} (x^{5} y^{\frac{3}{4}})

= lo g_{2} (x^{5} y^{\frac{3}{4}}) - lo g_{2} (z)

Apply log rule:

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

lo g_{2} (x^{5} y^{\frac{3}{4}}) - lo g_{2} (z) = lo g_{2} (\frac{x ^{5} y ^{\frac{3}{4}}}{z})

= lo g_{2} (\frac{x ^{5} y ^{\frac{3}{4}}}{z})

5 lo g_{10} (x) - 8 lo g_{10} (x + 1)

lo g_{4} (\frac{16}{x + 3})

\frac{2}{5} lo g_{10} (x) - lo g_{10} (y)

1 + ln (2 x)

What is 5log_{2}(x)+3/4 log_{2}(y)-log_{2}(z) ?
The solution to 5log_{2}(x)+3/4 log_{2}(y)-log_{2}(z) is log_{2}((x^5\sqrt[4]{y^3})/z)