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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

Simplify

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

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

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

lo g_{10} ((\frac{6}{11})^{5})

lo g_{2} (x - 2) + lo g_{2} (x + 3)

lo g_{2} (\frac{27}{3}) - lo g_{2} (\frac{16}{2})

lo g_{5} (\frac{x}{25})

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