What is log_{10}(x^2-17x+72)-log_{10}(x-9) ?

The solution to log_{10}(x^2-17x+72)-log_{10}(x-9) is log_{10}(x-8)

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simplify log_{10}(x^2-17x+72)-log_{10}(x-9)

simplify

lo g_{10} (x^{2} - 17 x + 72) - lo g_{10} (x - 9)

lo g_{10} (x - 8)

Solution steps

lo g_{10} (x^{2} - 17 x + 72) - lo g_{10} (x - 9)

Apply log rule:

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

lo g_{10} (x^{2} - 17 x + 72) - lo g_{10} (x - 9) = lo g_{10} (\frac{x ^{2} - 17 x + 72}{x - 9})

= lo g_{10} (\frac{x ^{2} - 17 x + 72}{x - 9})

Simplify

\frac{x ^{2} - 17 x + 72}{x - 9} : x - 8

= lo g_{10} (x - 8)

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What is log_{10}(x^2-17x+72)-log_{10}(x-9) ?
The solution to log_{10}(x^2-17x+72)-log_{10}(x-9) is log_{10}(x-8)