What is 4/3 ln|x-1|-1/3 ln|x-4| ?

The solution to 4/3 ln|x-1|-1/3 ln|x-4| is ln(\sqrt[3]{((x-1)^4)/(|x-4|)})

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simplify 4/3 ln|x-1|-1/3 ln|x-4|

simplify

\frac{4}{3} ln ∣ x - 1 ∣ - \frac{1}{3} ln ∣ x - 4 ∣

Solution steps

\frac{4}{3} ln ∣ x - 1 ∣ - \frac{1}{3} ln ∣ x - 4 ∣

Apply log rule:

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

\frac{4}{3} ln ∣ x - 1 ∣ = ln (∣ x - 1 ∣^{\frac{4}{3}})

= ln (∣ x - 1 ∣^{\frac{4}{3}}) - \frac{1}{3} ln ∣ x - 4 ∣

Apply log rule:

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

\frac{1}{3} ln ∣ x - 4 ∣ = ln (∣ x - 4 ∣^{\frac{1}{3}})

= ln (∣ x - 1 ∣^{\frac{4}{3}}) - ln (∣ x - 4 ∣^{\frac{1}{3}})

Apply log rule:

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

ln (∣ x - 1 ∣^{\frac{4}{3}}) - ln (∣ x - 4 ∣^{\frac{1}{3}}) = ln (\frac{∣ x - 1 ∣ ^{\frac{4}{3}}}{∣ x - 4 ∣ ^{\frac{1}{3}}})

= ln (\frac{∣ x - 1 ∣ ^{\frac{4}{3}}}{∣ x - 4 ∣ ^{\frac{1}{3}}})

Simplify

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What is 4/3 ln|x-1|-1/3 ln|x-4| ?
The solution to 4/3 ln|x-1|-1/3 ln|x-4| is ln(\sqrt[3]{((x-1)^4)/(|x-4|)})