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

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

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simplify 2log_{3}(x)-log_{3}(x-2)

simplify

2 lo g_{3} (x) - lo g_{3} (x - 2)

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

Solution steps

2 lo g_{3} (x) - lo g_{3} (x - 2)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 lo g_{3} (x) = lo g_{3} (x^{2})

= lo g_{3} (x^{2}) - lo g_{3} (x - 2)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

2 ln (a) - 5 ln (b) + ln (c)

ln (10 e^{- x})

ln (\frac{x ^{2} ( x + 1 )}{x + 2})

lo g_{10} (x^{5} z)

lo g_{2} (x^{3})

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