What is log_{10}(x^2+3x+2)-log_{10}(x^2-4) ?

The solution to log_{10}(x^2+3x+2)-log_{10}(x^2-4) is log_{10}((x+1)/(x-2))

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simplify log_{10}(x^2+3x+2)-log_{10}(x^2-4)

simplify

lo g_{10} (x^{2} + 3 x + 2) - lo g_{10} (x^{2} - 4)

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

Solution steps

lo g_{10} (x^{2} + 3 x + 2) - lo g_{10} (x^{2} - 4)

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^{2} - 4) = lo g_{10} (\frac{x ^{2} + 3 x + 2}{x ^{2} - 4})

= lo g_{10} (\frac{x ^{2} + 3 x + 2}{x ^{2} - 4})

Simplify

\frac{x ^{2} + 3 x + 2}{x ^{2} - 4} : \frac{x + 1}{x - 2}

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

lo g_{6} (x^{4} y^{3})

lo g_{a} (0.78) - lo g_{a} (6)

\frac{3}{4} lo g_{2} (x^{4}) - lo g_{2} (y)

- ln (\frac{2}{2}) + ln (1)

ln (\frac{x ^{4}}{( 3 x - 4 ) ^{2}})

What is log_{10}(x^2+3x+2)-log_{10}(x^2-4) ?
The solution to log_{10}(x^2+3x+2)-log_{10}(x^2-4) is log_{10}((x+1)/(x-2))