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

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

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

simplify

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

Solution steps

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

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 ∣

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}})

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}}})

Combine same powers :

lo g_{e} (9) + lo g_{e} (2)

ln (\frac{1}{2} x - 3 + x^{2} - 6 x + 13)

3 lo g_{9} (a) - 12 lo g_{9} (b)

3 ln ∣ x ∣ - 2 ln ∣ x + 11 ∣

\frac{3}{2} ln (t) + \frac{1}{2} ln (b) - 2 + ln (e^{2}) - 8 ln (m)

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