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

The solution to log_{10}(x^2-6x+5)-log_{10}(x-5) is log_{10}(x-1)

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

simplify

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

lo g_{10} (x - 1)

Solution steps

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

Apply log rule:

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

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

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

Simplify

\frac{x ^{2} - 6 x + 5}{x - 5} : x - 1

= lo g_{10} (x - 1)

lo g_{2} (\frac{1 0 ^{- 3}}{3})

ln (2) + \frac{1}{3} ln (125)

2 ln (x) + 2 ln (y)

- lo g_{10} (5.5 \cdot 1 0^{- 3})

ln (\frac{2 y ^{2}}{z ^{3}})

What is log_{10}(x^2-6x+5)-log_{10}(x-5) ?
The solution to log_{10}(x^2-6x+5)-log_{10}(x-5) is log_{10}(x-1)