What is simplify-3ln|x+4|+3ln|x-4|+2C ?

The solution to simplify-3ln|x+4|+3ln|x-4|+2C is ln((|x-4|^3)/(|x+4|^3))+2C

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simplify-3ln|x+4|+3ln|x-4|+2C

simplify

- 3 ln ∣ x + 4 ∣ + 3 ln ∣ x - 4 ∣ + 2 C

ln (\frac{∣ x - 4 ∣ ^{3}}{∣ x + 4 ∣ ^{3}}) + 2 C

Solution steps

- 3 ln ∣ x + 4 ∣ + 3 ln ∣ x - 4 ∣ + 2 C

Apply log rule:

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

3 ln ∣ x + 4 ∣ = ln (∣ x + 4 ∣^{3})

= - ln (∣ x + 4 ∣^{3}) + 3 ln ∣ x - 4 ∣ + 2 C

Apply log rule:

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

3 ln ∣ x - 4 ∣ = ln (∣ x - 4 ∣^{3})

= - ln (∣ x + 4 ∣^{3}) + ln (∣ x - 4 ∣^{3}) + 2 C

Apply log rule:

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

ln (∣ x - 4 ∣^{3}) - ln (∣ x + 4 ∣^{3}) = ln (\frac{∣ x - 4 ∣ ^{3}}{∣ x + 4 ∣ ^{3}})

= ln (\frac{∣ x - 4 ∣ ^{3}}{∣ x + 4 ∣ ^{3}}) + 2 C

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

- \frac{1}{3} ln (\frac{1}{10000000000000})

4.53759 + lo g_{10} (\frac{0.51}{0.16})

lo g_{10} (\frac{5}{1000})

lo g_{2} (16.0312 + 1) + lo g_{2} (16.0312 - 1)

What is simplify-3ln|x+4|+3ln|x-4|+2C ?
The solution to simplify-3ln|x+4|+3ln|x-4|+2C is ln((|x-4|^3)/(|x+4|^3))+2C