What is (log_{2}(x)-log_{2}(y))+6log_{2}(z) ?

The solution to (log_{2}(x)-log_{2}(y))+6log_{2}(z) is log_{2}((xz^6)/y)

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simplify (log_{2}(x)-log_{2}(y))+6log_{2}(z)

simplify

(lo g_{2} (x) - lo g_{2} (y)) + 6 lo g_{2} (z)

lo g_{2} (\frac{x z ^{6}}{y})

Solution steps

(lo g_{2} (x) - lo g_{2} (y)) + 6 lo g_{2} (z)

Apply rule:

(a) = a

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

= lo g_{2} (x) - lo g_{2} (y) + 6 lo g_{2} (z)

Apply log rule:

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

6 lo g_{2} (z) = lo g_{2} (z^{6})

= lo g_{2} (x) - lo g_{2} (y) + lo g_{2} (z^{6})

Apply log rule:

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

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

= lo g_{2} (\frac{x}{y}) + lo g_{2} (z^{6})

Apply log rule:

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

lo g_{2} (\frac{x}{y}) + lo g_{2} (z^{6}) = lo g_{2} (\frac{x}{y} z^{6})

= lo g_{2} (\frac{x}{y} z^{6})

Simplify

\frac{x}{y} z^{6} : \frac{x z ^{6}}{y}

= lo g_{2} (\frac{x z ^{6}}{y})

lo g_{3} ((7 g^{9} h^{5})^{2})

lo g_{6} (\frac{6}{y})

2 lo g_{b} (x) + 3 lo g_{b} (y)

lo g_{5} (\frac{125}{y})

\frac{2}{3} lo g_{10} (\frac{E}{1 0 ^{4.4}})

What is (log_{2}(x)-log_{2}(y))+6log_{2}(z) ?
The solution to (log_{2}(x)-log_{2}(y))+6log_{2}(z) is log_{2}((xz^6)/y)