What is log_{10}(x^2+2x-48)-log_{10}(x^2-64) ?

The solution to log_{10}(x^2+2x-48)-log_{10}(x^2-64) is log_{10}((x-6)/(x-8))

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simplify log_{10}(x^2+2x-48)-log_{10}(x^2-64)

simplify

lo g_{10} (x^{2} + 2 x - 48) - lo g_{10} (x^{2} - 64)

lo g_{10} (\frac{x - 6}{x - 8})

Solution steps

lo g_{10} (x^{2} + 2 x - 48) - 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} + 2 x - 48) - lo g_{10} (x^{2} - 64) = lo g_{10} (\frac{x ^{2} + 2 x - 48}{x ^{2} - 64})

= lo g_{10} (\frac{x ^{2} + 2 x - 48}{x ^{2} - 64})

Simplify

\frac{x ^{2} + 2 x - 48}{x ^{2} - 64} : \frac{x - 6}{x - 8}

= lo g_{10} (\frac{x - 6}{x - 8})

- lo g_{10} (3.2 \cdot 1 0^{- 10})

lo g_{10} (\frac{x ^{2} y}{w ^{5} z})

- lo g_{2} (\frac{3}{8})

- lo g_{10} (5.4 \cdot 1 0^{- 4})

What is log_{10}(x^2+2x-48)-log_{10}(x^2-64) ?
The solution to log_{10}(x^2+2x-48)-log_{10}(x^2-64) is log_{10}((x-6)/(x-8))