What is ln((4x^2-x-2)/(x^2(x+1))) ?

The solution to ln((4x^2-x-2)/(x^2(x+1))) is ln(4x^2-x-2)-2ln(x)-ln(x+1)

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simplify ln((4x^2-x-2)/(x^2(x+1)))

simplify

ln (\frac{4 x ^{2} - x - 2}{x ^{2} ( x + 1 )})

ln (4 x^{2} - x - 2) - 2 ln (x) - ln (x + 1)

Solution steps

ln (\frac{4 x ^{2} - x - 2}{x ^{2} ( x + 1 )})

Apply log rule:

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

ln (\frac{4 x ^{2} - x - 2}{x ^{2} ( x + 1 )}) = ln (4 x^{2} - x - 2) - ln (x^{2} (x + 1))

= ln (4 x^{2} - x - 2) - ln (x^{2} (x + 1))

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (x^{2} (x + 1)) = ln (x^{2}) + ln (x + 1)

= ln (4 x^{2} - x - 2) - (ln (x^{2}) + ln (x + 1))

Apply log rule:

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

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

= ln (4 x^{2} - x - 2) - (2 ln (x) + ln (x + 1))

- (2 ln (x) + ln (x + 1)) : - 2 ln (x) - ln (x + 1)

= ln (4 x^{2} - x - 2) - 2 ln (x) - ln (x + 1)

ln (\frac{315}{90})

lo g_{4} (e) - lo g_{4} (5 e) - lo g_{4} (4 e)

2 (- ln ∣ x + 3 ∣ + 2 ln ∣ x + 6 ∣) + C

- \frac{1}{2} ln (x) + ln (\frac{1}{x})

ln (y + 4) - ln (x + 3)

What is ln((4x^2-x-2)/(x^2(x+1))) ?
The solution to ln((4x^2-x-2)/(x^2(x+1))) is ln(4x^2-x-2)-2ln(x)-ln(x+1)