What is ((ln|x+4|-6ln|x-1|))/5 ?

The solution to ((ln|x+4|-6ln|x-1|))/5 is (ln((|x+4|)/((x-1)^6)))/5

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simplify ((ln|x+4|-6ln|x-1|))/5

simplify

\frac{( ln ∣ x + 4 ∣ - 6 ln ∣ x - 1 ∣ )}{5}

\frac{ln ( \frac{∣ x + 4 ∣}{( x - 1 ) ^{6}} )}{5}

Solution steps

\frac{( ln ∣ x + 4 ∣ - 6 ln ∣ x - 1 ∣ )}{5}

Apply log rule:

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

6 ln ∣ x - 1 ∣ = ln (∣ x - 1 ∣^{6})

= \frac{( ln ∣ x + 4 ∣ - ln ( ∣ x - 1 ∣ ^{6} ) )}{5}

Apply log rule:

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

ln ∣ x + 4 ∣ - ln (∣ x - 1 ∣^{6}) = ln (\frac{∣ x + 4 ∣}{∣ x - 1 ∣ ^{6}})

= \frac{ln ( \frac{∣ x + 4 ∣}{∣ x - 1 ∣ ^{6}} )}{5}

∣ x - 1 ∣^{6} = (x - 1)^{6}

= \frac{ln ( \frac{∣ x + 4 ∣}{( x - 1 ) ^{6}} )}{5}

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What is ((ln|x+4|-6ln|x-1|))/5 ?
The solution to ((ln|x+4|-6ln|x-1|))/5 is (ln((|x+4|)/((x-1)^6)))/5