What is log_{10}(x^2+9x+8)-log_{10}(x^2-64) ?

The solution to log_{10}(x^2+9x+8)-log_{10}(x^2-64) is log_{10}((x+1)/(x-8))

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simplify log_{10}(x^2+9x+8)-log_{10}(x^2-64)

simplify

lo g_{10} (x^{2} + 9 x + 8) - lo g_{10} (x^{2} - 64)

lo g_{10} (\frac{x + 1}{x - 8})

Solution steps

lo g_{10} (x^{2} + 9 x + 8) - lo g_{10} (x^{2} - 64)

Apply log rule:

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

lo g_{10} (x^{2} + 9 x + 8) - lo g_{10} (x^{2} - 64) = lo g_{10} (\frac{x ^{2} + 9 x + 8}{x ^{2} - 64})

= lo g_{10} (\frac{x ^{2} + 9 x + 8}{x ^{2} - 64})

Simplify

\frac{x ^{2} + 9 x + 8}{x ^{2} - 64} : \frac{x + 1}{x - 8}

= lo g_{10} (\frac{x + 1}{x - 8})

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What is log_{10}(x^2+9x+8)-log_{10}(x^2-64) ?
The solution to log_{10}(x^2+9x+8)-log_{10}(x^2-64) is log_{10}((x+1)/(x-8))