What is log_{10}(x^2-2x-15)-log_{10}(x+3) ?

The solution to log_{10}(x^2-2x-15)-log_{10}(x+3) is log_{10}(x-5)

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simplify log_{10}(x^2-2x-15)-log_{10}(x+3)

simplify

lo g_{10} (x^{2} - 2 x - 15) - lo g_{10} (x + 3)

lo g_{10} (x - 5)

Solution steps

lo g_{10} (x^{2} - 2 x - 15) - lo g_{10} (x + 3)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (x^{2} - 2 x - 15) - lo g_{10} (x + 3) = lo g_{10} (\frac{x ^{2} - 2 x - 15}{x + 3})

= lo g_{10} (\frac{x ^{2} - 2 x - 15}{x + 3})

Simplify

\frac{x ^{2} - 2 x - 15}{x + 3} : x - 5

= lo g_{10} (x - 5)

lo g_{3} (\frac{x}{27})

ln (- i e^{14})

\frac{8}{12} lo g_{10} (\frac{8}{12}) + \frac{4}{12} lo g_{10} (\frac{4}{12})

ln (\frac{x ^{5}}{x ( 1 + x ) ^{3}})

What is log_{10}(x^2-2x-15)-log_{10}(x+3) ?
The solution to log_{10}(x^2-2x-15)-log_{10}(x+3) is log_{10}(x-5)