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

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

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

simplify

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

lo g_{a} (x + 2)

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

= lo g_{a} (x + 2)

lo g_{4} (\frac{5 x}{y})

lo g_{10} (1000000 y)

lo g_{3} (11 x (3 x + 4))

ln (x^{11} 2 - x)

lo g_{5} (x) - lo g_{5} (x^{6})

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