What is log_{10}(x^2-5x+6)-log_{10}(x-3) ?

The solution to log_{10}(x^2-5x+6)-log_{10}(x-3) is log_{10}(x-2)

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simplify log_{10}(x^2-5x+6)-log_{10}(x-3)

simplify

lo g_{10} (x^{2} - 5 x + 6) - lo g_{10} (x - 3)

lo g_{10} (x - 2)

Solution steps

lo g_{10} (x^{2} - 5 x + 6) - lo g_{10} (x - 3)

Apply log rule:

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

lo g_{10} (x^{2} - 5 x + 6) - lo g_{10} (x - 3) = lo g_{10} (\frac{x ^{2} - 5 x + 6}{x - 3})

= lo g_{10} (\frac{x ^{2} - 5 x + 6}{x - 3})

Simplify

\frac{x ^{2} - 5 x + 6}{x - 3} : x - 2

= lo g_{10} (x - 2)

lo g_{6} (a b^{3} c^{- 2})

2 lo g_{2^{x}} (+ 4 lo g_{2^{y}} (- 6 lo g_{2^{z}} (x)))

ln (\frac{1.5 \cdot 1 0 ^{11}}{1 0 ^{- 3}})

2.34 + lo g_{10} (\frac{1 \cdot 1 0 ^{- 7}}{0.1})

What is log_{10}(x^2-5x+6)-log_{10}(x-3) ?
The solution to log_{10}(x^2-5x+6)-log_{10}(x-3) is log_{10}(x-2)