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

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

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

simplify

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

lo g_{2} (x - 2)

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

= lo g_{2} (x - 2)

2 lo g_{10} (3) + lo g_{10} (2)

3 ln (x) - 6 ln (y)

\frac{1}{5} ln (x) + ln (y)

lo g_{4} (8) + 2 lo g_{4} (9)

2 lo g_{10} (x) - 3 lo g_{10} (x + 1)

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