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Popular >

simplify ln((x^2-1)/(x^9))

Solution

simplify

ln (\frac{x ^{2} - 1}{x ^{9}})

Solution

ln (x^{2} - 1) - 9 ln (x)

Solution steps

ln (\frac{x ^{2} - 1}{x ^{9}})

Apply log rule:

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

ln (\frac{x ^{2} - 1}{x ^{9}}) = ln (x^{2} - 1) - ln (x^{9})

= ln (x^{2} - 1) - ln (x^{9})

Apply log rule:

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

ln (x^{9}) = 9 ln (x)

= ln (x^{2} - 1) - 9 ln (x)

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Frequently Asked Questions (FAQ)

What is ln((x^2-1)/(x^9)) ?
The solution to ln((x^2-1)/(x^9)) is ln(x^2-1)-9ln(x)