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Popular >

simplify ln((n!)/(x^{n+1)})

Solution

simplify

ln (\frac{n !}{x ^{n + 1}})

Solution

ln (n!) - (n + 1) ln (x)

Solution steps

ln (\frac{n !}{x ^{n + 1}})

Apply log rule:

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

ln (\frac{n !}{x ^{n + 1}}) = ln (n!) - ln (x^{n + 1})

= ln (n!) - ln (x^{n + 1})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{n + 1}) = (n + 1) ln (x)

= ln (n!) - (n + 1) ln (x)

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Frequently Asked Questions (FAQ)

What is ln((n!)/(x^{n+1)}) ?
The solution to ln((n!)/(x^{n+1)}) is ln(n!)-(n+1)ln(x)