What is log_{3}(x^2-4)-log_{3}(x+2) ?

The solution to log_{3}(x^2-4)-log_{3}(x+2) is log_{3}(x-2)

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simplify log_{3}(x^2-4)-log_{3}(x+2)

simplify

lo g_{3} (x^{2} - 4) - lo g_{3} (x + 2)

lo g_{3} (x - 2)

Solution steps

lo g_{3} (x^{2} - 4) - lo g_{3} (x + 2)

Apply log rule:

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

lo g_{3} (x^{2} - 4) - lo g_{3} (x + 2) = lo g_{3} (\frac{x ^{2} - 4}{x + 2})

= lo g_{3} (\frac{x ^{2} - 4}{x + 2})

Simplify

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

= lo g_{3} (x - 2)

lo g_{10} (\frac{a ^{2}}{b ^{4} c})

lo g_{3} (5) + 5 lo g_{3} (2)

lo g_{4} (3) + lo g_{4} (5)

lo g_{3} (x y)

lo g_{7} (3 x)

What is log_{3}(x^2-4)-log_{3}(x+2) ?
The solution to log_{3}(x^2-4)-log_{3}(x+2) is log_{3}(x-2)