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

The solution to log_{10}(x^2-x-12)-log_{10}(x^2-7x+12) is log_{10}((x+3)/(x-3))

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

simplify

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

lo g_{10} (\frac{x + 3}{x - 3})

Solution steps

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

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

Simplify

\frac{x ^{2} - x - 12}{x ^{2} - 7 x + 12} : \frac{x + 3}{x - 3}

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

lo g_{4} (x) - lo g_{4} (7 y)

lo g_{7} (3 x^{4} y^{3}) - lo g_{7} (5 x^{6} y^{3})

- lo g_{10} (1.6 \cdot 1 0^{- 2})

3 lo g_{10} (a) - lo g_{10} (b)

ln ∣ sin (x) ∣ + ln ∣ sec (x) ∣

What is log_{10}(x^2-x-12)-log_{10}(x^2-7x+12) ?
The solution to log_{10}(x^2-x-12)-log_{10}(x^2-7x+12) is log_{10}((x+3)/(x-3))