What is sqrt(|5x+2|-|x^2+2|)+ln(4x) ?

The solution to sqrt(|5x+2|-|x^2+2|)+ln(4x) is sqrt(|5x+2|-|x^2+2|)+2ln(2)+ln(x)

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simplify sqrt(|5x+2|-|x^2+2|)+ln(4x)

simplify

∣ 5 x + 2 ∣ - ∣ x^{2} + 2 ∣ + ln (4 x)

∣ 5 x + 2 ∣ - ∣ x^{2} + 2 ∣ + 2 ln (2) + ln (x)

Solution steps

∣ 5 x + 2 ∣ - ∣ x^{2} + 2 ∣ + ln (4 x)

Apply log rule:

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

ln (4 x) = ln (4) + ln (x)

= ∣ 5 x + 2 ∣ - ∣ x^{2} + 2 ∣ + ln (4) + ln (x)

ln (4) = 2 ln (2)

= ∣ 5 x + 2 ∣ - ∣ x^{2} + 2 ∣ + 2 ln (2) + ln (x)

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

1.03 ln (2.538 x)

ln (x - 4) [ln (x + 3) + ln (x - 5)]

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

\frac{1}{4} ln (\frac{3 tan ( \frac{x}{2} + 1 )}{tan ( \frac{x}{2} + 3 )}) + c

What is sqrt(|5x+2|-|x^2+2|)+ln(4x) ?
The solution to sqrt(|5x+2|-|x^2+2|)+ln(4x) is sqrt(|5x+2|-|x^2+2|)+2ln(2)+ln(x)