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

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

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simplify log_{3}((x^4)/(x-4))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

= lo g_{3} (x^{4}) - lo g_{3} (x - 4)

Simplify

lo g_{3} (x^{4}) : 4 lo g_{3} (x)

= 4 lo g_{3} (x) - lo g_{3} (x - 4)

lo g_{10} (7) + lo g_{10} (3)

ln (x^{12} 6 - x)

lo g_{10} (7) + lo g_{10} (4)

lo g_{a} (\frac{x y}{z ^{2}})

ln (x e^{5 x})

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