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Popular >

simplify ln(1/(x^n))

Solution

simplify

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

Solution

- n ln (x)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (1) - n ln (x)

Apply log rule:

lo g_{a} (1) = 0

= 0 - n ln (x)

0 - n ln (x) = - n ln (x)

= - n ln (x)

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Frequently Asked Questions (FAQ)

What is ln(1/(x^n)) ?
The solution to ln(1/(x^n)) is -nln(x)