What is simplify-1/3 ln|x+1|+1/3 ln|x-2|+3 ?

The solution to simplify-1/3 ln|x+1|+1/3 ln|x-2|+3 is ln(\sqrt[3]{(|x-2|)/(|x+1|)})+3

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simplify-1/3 ln|x+1|+1/3 ln|x-2|+3

simplify

- \frac{1}{3} ln ∣ x + 1 ∣ + \frac{1}{3} ln ∣ x - 2 ∣ + 3

Solution steps

- \frac{1}{3} ln ∣ x + 1 ∣ + \frac{1}{3} ln ∣ x - 2 ∣ + 3

Apply log rule:

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

\frac{1}{3} ln ∣ x + 1 ∣ = ln (∣ x + 1 ∣^{\frac{1}{3}})

= - ln (∣ x + 1 ∣^{\frac{1}{3}}) + \frac{1}{3} ln ∣ x - 2 ∣ + 3

Apply log rule:

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

\frac{1}{3} ln ∣ x - 2 ∣ = ln (∣ x - 2 ∣^{\frac{1}{3}})

= - ln (∣ x + 1 ∣^{\frac{1}{3}}) + ln (∣ x - 2 ∣^{\frac{1}{3}}) + 3

Apply log rule:

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

ln (∣ x - 2 ∣^{\frac{1}{3}}) - ln (∣ x + 1 ∣^{\frac{1}{3}}) = ln (\frac{∣ x - 2 ∣ ^{\frac{1}{3}}}{∣ x + 1 ∣ ^{\frac{1}{3}}})

= ln (\frac{∣ x - 2 ∣ ^{\frac{1}{3}}}{∣ x + 1 ∣ ^{\frac{1}{3}}}) + 3

Combine same powers :

ln (6) + ln (\frac{e ^{(2.43849)}}{3})

ln (7 (- 4)^{2} (2) (3))

ln (\frac{96}{7}) + \frac{1}{2} (ln (\frac{2}{3} x)) + \frac{1}{4} (ln (\frac{15}{8}))

lo g_{10} (2 π \cdot 1606 \cdot 5.03 \cdot 9.566)

4 (ln (2) - 3 ln (a))

What is simplify-1/3 ln|x+1|+1/3 ln|x-2|+3 ?
The solution to simplify-1/3 ln|x+1|+1/3 ln|x-2|+3 is ln(\sqrt[3]{(|x-2|)/(|x+1|)})+3