What is log_{10}(2x^2-5x-3)-log_{10}(x^2-7x+12) ?

The solution to log_{10}(2x^2-5x-3)-log_{10}(x^2-7x+12) is log_{10}((2x+1)/(x-4))

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simplify log_{10}(2x^2-5x-3)-log_{10}(x^2-7x+12)

simplify

lo g_{10} (2 x^{2} - 5 x - 3) - lo g_{10} (x^{2} - 7 x + 12)

lo g_{10} (\frac{2 x + 1}{x - 4})

Solution steps

lo g_{10} (2 x^{2} - 5 x - 3) - 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} (2 x^{2} - 5 x - 3) - lo g_{10} (x^{2} - 7 x + 12) = lo g_{10} (\frac{2 x ^{2} - 5 x - 3}{x ^{2} - 7 x + 12})

= lo g_{10} (\frac{2 x ^{2} - 5 x - 3}{x ^{2} - 7 x + 12})

Simplify

\frac{2 x ^{2} - 5 x - 3}{x ^{2} - 7 x + 12} : \frac{2 x + 1}{x - 4}

= lo g_{10} (\frac{2 x + 1}{x - 4})

ln (v^{'} (t) - \frac{m ( t ) g ( m ( t ) )}{b}) - ln (- \frac{m ( t ) g ( m ( t ) )}{b})

lo g_{b} (\frac{b b}{( c + 1 ) ^{3}})

2 ln (x) - 3 ln (x - 1) - ln (x)

lo g_{2} (x) + 3 lo g_{2} (x + 2)

lo g_{2} (32 x^{3})

What is log_{10}(2x^2-5x-3)-log_{10}(x^2-7x+12) ?
The solution to log_{10}(2x^2-5x-3)-log_{10}(x^2-7x+12) is log_{10}((2x+1)/(x-4))