What is ln|x|+2ln|x^2+4|+C ?

The solution to ln|x|+2ln|x^2+4|+C is ln(|x|(x^2+4)^2)+C

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simplify ln|x|+2ln|x^2+4|+C

simplify

ln ∣ x ∣ + 2 ln x^{2} + 4 + C

ln (∣ x ∣ (x^{2} + 4)^{2}) + C

Solution steps

ln ∣ x ∣ + 2 ln x^{2} + 4 + C

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln ∣ x ∣ + ln (x^{2} + 4^{2}) + C

Apply log rule:

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

ln ∣ x ∣ + ln (x^{2} + 4^{2}) = ln (∣ x ∣ x^{2} + 4^{2})

= ln (∣ x ∣ x^{2} + 4^{2}) + C

x^{2} + 4^{2} = (x^{2} + 4)^{2}

= ln (∣ x ∣ (x^{2} + 4)^{2}) + C

- ln (6) + ln (5) + ln (5) - 2 ln (2)

2 ln (5) + 2 ln (2)

ln (- e^{- 2} \cdot 0.2)

lo g_{10} (- 6 i)

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

What is ln|x|+2ln|x^2+4|+C ?
The solution to ln|x|+2ln|x^2+4|+C is ln(|x|(x^2+4)^2)+C