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

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

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

simplify

ln (∣ x ∣ (x^{2} + 4)^{2}) + C

ln ∣ x ∣ + 2 ln (x^{2} + 4) + C

Solution steps

ln (∣ x ∣ (x^{2} + 4)^{2}) + C

Apply log rule:

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

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

= ln ∣ x ∣ + ln ((x^{2} + 4)^{2}) + C

Apply log rule:

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

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

= ln ∣ x ∣ + 2 ln (x^{2} + 4) + C

- lo g_{10} (2.6 \cdot 1 0^{- 2})

lo g_{e} (\frac{9}{10})

2 (lo g_{m} (x) - 5 lo g_{m} (y)) + 2 lo g_{m} (z)

lo g_{10} (0.98 \cdot 111.2 \cdot 1 0^{- 6} \cdot 2 π \cdot 200.27)

- \frac{8.5}{30} ln (\frac{1}{2})

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