What is 2*ln|x-1|+5*ln|x+4|+C ?

The solution to 2*ln|x-1|+5*ln|x+4|+C is ln(|x+4|^5(x-1)^2)+C

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simplify 2ln|x-1|+5ln|x+4|+C

simplify

2 \cdot ln ∣ x - 1 ∣ + 5 \cdot ln ∣ x + 4 ∣ + C

ln (∣ x + 4 ∣^{5} (x - 1)^{2}) + C

Solution steps

2 ln ∣ x - 1 ∣ + 5 ln ∣ x + 4 ∣ + C

Apply log rule:

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

2 ln ∣ x - 1 ∣ = ln (∣ x - 1 ∣^{2})

= ln (∣ x - 1 ∣^{2}) + 5 ln ∣ x + 4 ∣ + C

Apply log rule:

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

5 ln ∣ x + 4 ∣ = ln (∣ x + 4 ∣^{5})

= ln (∣ x - 1 ∣^{2}) + ln (∣ x + 4 ∣^{5}) + C

Apply log rule:

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

ln (∣ x - 1 ∣^{2}) + ln (∣ x + 4 ∣^{5}) = ln (∣ x + 4 ∣^{5} ∣ x - 1 ∣^{2})

= ln (∣ x + 4 ∣^{5} ∣ x - 1 ∣^{2}) + C

∣ x - 1 ∣^{2} = (x - 1)^{2}

= ln (∣ x + 4 ∣^{5} (x - 1)^{2}) + C

3 + ln ((\frac{3}{2})^{- 3}) - 3 + ln (2^{2})

ln (353) - ln (277)

\frac{1}{3} lo g_{6} (x) + 2 lo g_{6} (x + 1) + 3

(\frac{17}{12})^{2} ln (\frac{17}{12})

lo g_{4} (\frac{e ^{x} + 9}{- 4})

What is 2*ln|x-1|+5*ln|x+4|+C ?
The solution to 2*ln|x-1|+5*ln|x+4|+C is ln(|x+4|^5(x-1)^2)+C