What is log_{3}(x^2-1)-log_{3}(x+1) ?

The solution to log_{3}(x^2-1)-log_{3}(x+1) is log_{3}(x-1)

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simplify log_{3}(x^2-1)-log_{3}(x+1)

simplify

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

lo g_{3} (x - 1)

Solution steps

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

Apply log rule:

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

lo g_{3} (x^{2} - 1) - lo g_{3} (x + 1) = lo g_{3} (\frac{x ^{2} - 1}{x + 1})

= lo g_{3} (\frac{x ^{2} - 1}{x + 1})

Simplify

\frac{x ^{2} - 1}{x + 1} : x - 1

= lo g_{3} (x - 1)

\frac{1}{3} [5 ln (x + 6) - ln (x) - ln (x^{2} - 25)]

ln (\frac{x}{x - 1})

ln (\frac{e x ^{8}}{y})

lo g_{6} (36 x^{7})

lo g_{3} (a) + lo g_{3} (a + 6)

What is log_{3}(x^2-1)-log_{3}(x+1) ?
The solution to log_{3}(x^2-1)-log_{3}(x+1) is log_{3}(x-1)