What is log_{5}((x^{11})/(x-7)) ?

The solution to log_{5}((x^{11})/(x-7)) is 11log_{5}(x)-log_{5}(x-7)

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simplify log_{5}((x^{11})/(x-7))

simplify

lo g_{5} (\frac{x ^{11}}{x - 7})

11 lo g_{5} (x) - lo g_{5} (x - 7)

Solution steps

lo g_{5} (\frac{x ^{11}}{x - 7})

Apply log rule:

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

lo g_{5} (\frac{x ^{11}}{x - 7}) = lo g_{5} (x^{11}) - lo g_{5} (x - 7)

= lo g_{5} (x^{11}) - lo g_{5} (x - 7)

Simplify

lo g_{5} (x^{11}) : 11 lo g_{5} (x)

= 11 lo g_{5} (x) - lo g_{5} (x - 7)

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What is log_{5}((x^{11})/(x-7)) ?
The solution to log_{5}((x^{11})/(x-7)) is 11log_{5}(x)-log_{5}(x-7)