What is 3ln|x+3|-ln|x-3|+C ?

The solution to 3ln|x+3|-ln|x-3|+C is ln((|x+3|^3)/(|x-3|))+C

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simplify 3ln|x+3|-ln|x-3|+C

simplify

3 ln ∣ x + 3 ∣ - ln ∣ x - 3 ∣ + C

ln (\frac{∣ x + 3 ∣ ^{3}}{∣ x - 3 ∣}) + C

Solution steps

3 ln ∣ x + 3 ∣ - ln ∣ x - 3 ∣ + C

Apply log rule:

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

3 ln ∣ x + 3 ∣ = ln (∣ x + 3 ∣^{3})

= ln (∣ x + 3 ∣^{3}) - ln ∣ x - 3 ∣ + C

Apply log rule:

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

ln (∣ x + 3 ∣^{3}) - ln ∣ x - 3 ∣ = ln (\frac{∣ x + 3 ∣ ^{3}}{∣ x - 3 ∣})

= ln (\frac{∣ x + 3 ∣ ^{3}}{∣ x - 3 ∣}) + C

7 lo g_{5} (6 e) + 5 lo g_{5} (2 e)

20 \cdot lo g_{10} (\frac{1}{2 π ^{0} + 1})

- (\frac{5}{11}) \cdot ln (\frac{5}{11})

lo g_{8} (\frac{5 ^{2}}{6 \cdot 7}) 6

6 lo g_{3} (y) - \frac{1}{4} lo g_{3} (x) + 2 lo g_{3} (w)

What is 3ln|x+3|-ln|x-3|+C ?
The solution to 3ln|x+3|-ln|x-3|+C is ln((|x+3|^3)/(|x-3|))+C