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

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

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

simplify

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

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

Solution steps

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

Apply rule:

(a) = a

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

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

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

5 x - 8 = 0

\frac{x}{2} + 2 x + 3 x = 55

\frac{3 y ^{4} - 3 y ^{2} - 30 y}{( 3 y ^{2} ) ^{2}}

m^{2} + 2 m + 1

- 4 b^{2} + 4 b - 14 = - 5 b^{2}

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