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

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

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

simplify

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

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

Solution steps

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

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

lo g_{2} (\frac{x ^{3}}{x + 5})

- \frac{18 ln ( 2 )}{ln ( \frac{8}{5} )}

ln (5) + 3 ln (x) + 5 ln (x^{2} + 6)

lo g_{5} (\frac{x y}{z t})

\frac{1}{2} ln (9) - 3 ln (6) + 3 ln (2)

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