What is log_{10}(x^2+2x-15)-log_{10}(x^2-7x+12) ?

The solution to log_{10}(x^2+2x-15)-log_{10}(x^2-7x+12) is log_{10}((x+5)/(x-4))

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simplify log_{10}(x^2+2x-15)-log_{10}(x^2-7x+12)

simplify

lo g_{10} (x^{2} + 2 x - 15) - lo g_{10} (x^{2} - 7 x + 12)

lo g_{10} (\frac{x + 5}{x - 4})

Solution steps

lo g_{10} (x^{2} + 2 x - 15) - lo g_{10} (x^{2} - 7 x + 12)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{10} (x^{2} + 2 x - 15) - lo g_{10} (x^{2} - 7 x + 12) = lo g_{10} (\frac{x ^{2} + 2 x - 15}{x ^{2} - 7 x + 12})

= lo g_{10} (\frac{x ^{2} + 2 x - 15}{x ^{2} - 7 x + 12})

Simplify

\frac{x ^{2} + 2 x - 15}{x ^{2} - 7 x + 12} : \frac{x + 5}{x - 4}

= lo g_{10} (\frac{x + 5}{x - 4})

lo g_{a} (40) + lo g_{a} (4)

lo g_{8} (x \cdot y \cdot z^{3})

ln (y \frac{y}{8 - y})

\frac{1}{2} (ln (8) x^{2} - ln (4) - 3 ln (x) - ln (y))

lo g_{3} (x) - lo g_{3} (y) - lo g_{3} (z)

What is log_{10}(x^2+2x-15)-log_{10}(x^2-7x+12) ?
The solution to log_{10}(x^2+2x-15)-log_{10}(x^2-7x+12) is log_{10}((x+5)/(x-4))