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Popular >

simplify ln((x^2)/((x-1)^3))

Solution

simplify

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

Solution

2 ln (x) - 3 ln (x - 1)

Solution steps

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

Apply log rule:

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

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

= ln (x^{2}) - ln ((x - 1)^{3})

Apply log rule:

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

ln (x^{2}) = 2 ln (x)

= 2 ln (x) - ln ((x - 1)^{3})

Apply log rule:

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

ln ((x - 1)^{3}) = 3 ln (x - 1)

= 2 ln (x) - 3 ln (x - 1)

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Frequently Asked Questions (FAQ)

What is ln((x^2)/((x-1)^3)) ?
The solution to ln((x^2)/((x-1)^3)) is 2ln(x)-3ln(x-1)