What is log_{10}(x^2-4)-log_{10}(x-2) ?

The solution to log_{10}(x^2-4)-log_{10}(x-2) is log_{10}(x+2)

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simplify log_{10}(x^2-4)-log_{10}(x-2)

simplify

lo g_{10} (x^{2} - 4) - lo g_{10} (x - 2)

lo g_{10} (x + 2)

Solution steps

lo g_{10} (x^{2} - 4) - lo g_{10} (x - 2)

Apply log rule:

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

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

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

Simplify

\frac{x ^{2} - 4}{x - 2} : x + 2

= lo g_{10} (x + 2)

ln (\frac{( x + 3 )}{x y})

\frac{1}{4} + ln (\frac{π}{3})

lo g_{8} (11 x)

lo g_{3} (\frac{81 x}{x ^{2} + 9})

lo g_{2} (\frac{z}{4})

What is log_{10}(x^2-4)-log_{10}(x-2) ?
The solution to log_{10}(x^2-4)-log_{10}(x-2) is log_{10}(x+2)