What is log_{10}(x^2-x-6)-log_{10}(x^2-5x+6) ?

The solution to log_{10}(x^2-x-6)-log_{10}(x^2-5x+6) is log_{10}((x+2)/(x-2))

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simplify log_{10}(x^2-x-6)-log_{10}(x^2-5x+6)

simplify

lo g_{10} (x^{2} - x - 6) - lo g_{10} (x^{2} - 5 x + 6)

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

Solution steps

lo g_{10} (x^{2} - x - 6) - lo g_{10} (x^{2} - 5 x + 6)

Apply log rule:

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

lo g_{10} (x^{2} - x - 6) - lo g_{10} (x^{2} - 5 x + 6) = lo g_{10} (\frac{x ^{2} - x - 6}{x ^{2} - 5 x + 6})

= lo g_{10} (\frac{x ^{2} - x - 6}{x ^{2} - 5 x + 6})

Simplify

\frac{x ^{2} - x - 6}{x ^{2} - 5 x + 6} : \frac{x + 2}{x - 2}

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

2 lo g_{10} (a) + 3 lo g_{10} (b) - 4 lo g_{10} (c)

ln (5) + ln (x - 1)

13.375 ln (\frac{x}{x - 1250})

\frac{ln ( 3 ) + ln ( 32 )}{ln ( 3 ) - ln ( 16 )}

- lo g_{10} (1.7 \cdot 1 0^{- 3})

What is log_{10}(x^2-x-6)-log_{10}(x^2-5x+6) ?
The solution to log_{10}(x^2-x-6)-log_{10}(x^2-5x+6) is log_{10}((x+2)/(x-2))