What is 5(-ln|1-4|+ln|1-5|)+y+C ?

The solution to 5(-ln|1-4|+ln|1-5|)+y+C is 5ln(4/3)+y+C

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simplify 5(-ln|1-4|+ln|1-5|)+y+C

simplify

5 (- ln ∣ 1 - 4 ∣ + ln ∣ 1 - 5 ∣) + y + C

5 ln (\frac{4}{3}) + y + C

Solution steps

5 (- ln ∣ 1 - 4 ∣ + ln ∣ 1 - 5 ∣) + y + C

Apply log rule:

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

ln ∣ 1 - 5 ∣ - ln ∣ 1 - 4 ∣ = ln (\frac{∣ 1 - 5 ∣}{∣ 1 - 4 ∣})

= 5 (ln (\frac{∣ 1 - 5 ∣}{∣ 1 - 4 ∣})) + y + C

\frac{∣ 1 - 5 ∣}{∣ 1 - 4 ∣} = \frac{4}{3}

= 5 (ln (\frac{4}{3})) + y + C

Remove parentheses:

(a) = a

= 5 ln (\frac{4}{3}) + y + C

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What is 5(-ln|1-4|+ln|1-5|)+y+C ?
The solution to 5(-ln|1-4|+ln|1-5|)+y+C is 5ln(4/3)+y+C