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

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

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

simplify

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

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

Solution steps

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

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 + 4)

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

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

ln (\frac{x ^{2}}{e ^{x c o s (x)}})

lo g_{8} (\frac{x ^{3}}{5})

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

- \frac{1}{3} + \frac{1}{3} ln (\frac{3 + 5}{2})

3 ln (2) - 2 ln (3)

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