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})

lo g_{2} (\frac{4}{x + 4})

ln (x) + 4 ln (y)

ln (x) + 2 ln (y)

- lo g_{10} (1.3 \cdot 1 0^{- 5})

lo g_{10} (\frac{y}{x ^{4} z ^{5}})

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))