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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{x ^{3}}{y} z : \frac{x ^{3} z}{y}

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

ln (\frac{1}{16 e ^{2}})

10 lo g_{10} (x) - 2 lo g_{10} (x^{2})

lo g_{10} (\frac{c}{a ^{4} b ^{4}})

lo g_{10} (5 x y^{2})

lo g_{10} (\frac{y}{1})

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