What is 2(log_{a}(x)-log_{a}(y+1)+log_{a}(z)) ?

The solution to 2(log_{a}(x)-log_{a}(y+1)+log_{a}(z)) is 2log_{a}((xz)/(y+1))

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simplify 2(log_{a}(x)-log_{a}(y+1)+log_{a}(z))

simplify

2 (lo g_{a} (x) - lo g_{a} (y + 1) + lo g_{a} (z))

2 lo g_{a} (\frac{x z}{y + 1})

Solution steps

2 (lo g_{a} (x) - lo g_{a} (y + 1) + lo g_{a} (z))

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 + 1) = lo g_{a} (\frac{x}{y + 1})

= 2 (lo g_{a} (\frac{x}{y + 1}) + lo g_{a} (z))

Apply log rule:

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

lo g_{a} (\frac{x}{y + 1}) + lo g_{a} (z) = lo g_{a} (\frac{x}{y + 1} z)

= 2 lo g_{a} (\frac{x}{y + 1} z)

Simplify

\frac{x}{y + 1} z : \frac{x z}{y + 1}

= 2 lo g_{a} (\frac{x z}{y + 1})

\frac{1}{2} (lo g_{2} (a) + lo g_{2} (b))

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

ln (x) - ln (\frac{1}{x})

0.7 \cdot lo g_{10} (1 \cdot 1 0^{- 3}) + 0.1

lo g_{2} (x^{2} - 1) - lo g_{2} (x + 1)

What is 2(log_{a}(x)-log_{a}(y+1)+log_{a}(z)) ?
The solution to 2(log_{a}(x)-log_{a}(y+1)+log_{a}(z)) is 2log_{a}((xz)/(y+1))