What is log_{3}((x^{14})/(x-2)) ?

The solution to log_{3}((x^{14})/(x-2)) is 14log_{3}(x)-log_{3}(x-2)

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simplify log_{3}((x^{14})/(x-2))

simplify

lo g_{3} (\frac{x ^{14}}{x - 2})

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

Solution steps

lo g_{3} (\frac{x ^{14}}{x - 2})

Apply log rule:

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

lo g_{3} (\frac{x ^{14}}{x - 2}) = lo g_{3} (x^{14}) - lo g_{3} (x - 2)

= lo g_{3} (x^{14}) - lo g_{3} (x - 2)

Simplify

lo g_{3} (x^{14}) : 14 lo g_{3} (x)

= 14 lo g_{3} (x) - lo g_{3} (x - 2)

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

\frac{1}{2} ln (11)

lo g_{7} (\frac{f}{12})

\frac{1}{2} ln (12)

lo g_{4} (\frac{64}{x + 5})

What is log_{3}((x^{14})/(x-2)) ?
The solution to log_{3}((x^{14})/(x-2)) is 14log_{3}(x)-log_{3}(x-2)