What is log_{10}(x^2+3x+2)-log_{10}(x+1) ?

The solution to log_{10}(x^2+3x+2)-log_{10}(x+1) is log_{10}(x+2)

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simplify log_{10}(x^2+3x+2)-log_{10}(x+1)

simplify

lo g_{10} (x^{2} + 3 x + 2) - lo g_{10} (x + 1)

lo g_{10} (x + 2)

Solution steps

lo g_{10} (x^{2} + 3 x + 2) - lo g_{10} (x + 1)

Apply log rule:

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

lo g_{10} (x^{2} + 3 x + 2) - lo g_{10} (x + 1) = lo g_{10} (\frac{x ^{2} + 3 x + 2}{x + 1})

= lo g_{10} (\frac{x ^{2} + 3 x + 2}{x + 1})

Simplify

\frac{x ^{2} + 3 x + 2}{x + 1} : x + 2

= lo g_{10} (x + 2)

2 lo g_{3} (u) + 7 lo g_{3} (v)

lo g_{10} (\frac{c ^{3}}{a ^{2} b ^{3}})

lo g_{10} (\frac{x ^{2} + 1}{x + 3})

lo g_{6} (\frac{5 x ^{3}}{y})

ln (\frac{73}{165})

What is log_{10}(x^2+3x+2)-log_{10}(x+1) ?
The solution to log_{10}(x^2+3x+2)-log_{10}(x+1) is log_{10}(x+2)