What is simplify-1/5 ln|y+1|+1/5 ln|y-4| ?

The solution to simplify-1/5 ln|y+1|+1/5 ln|y-4| is ln(\sqrt[5]{(|y-4|)/(|y+1|)})

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simplify-1/5 ln|y+1|+1/5 ln|y-4|

simplify

- \frac{1}{5} ln ∣ y + 1 ∣ + \frac{1}{5} ln ∣ y - 4 ∣

Solution steps

- \frac{1}{5} ln ∣ y + 1 ∣ + \frac{1}{5} ln ∣ y - 4 ∣

Apply log rule:

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

\frac{1}{5} ln ∣ y + 1 ∣ = ln (∣ y + 1 ∣^{\frac{1}{5}})

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

Apply log rule:

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

\frac{1}{5} ln ∣ y - 4 ∣ = ln (∣ y - 4 ∣^{\frac{1}{5}})

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

Apply log rule:

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

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

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

Combine same powers :

- lo g_{10} (6.35 \cdot 1 0^{- 8})

3 \cdot lo g_{e} (10 x)

3 ln (1 + 2)

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

ln (x) - \frac{1}{2} ln (\frac{y}{x}) - \frac{y}{3 x}

What is simplify-1/5 ln|y+1|+1/5 ln|y-4| ?
The solution to simplify-1/5 ln|y+1|+1/5 ln|y-4| is ln(\sqrt[5]{(|y-4|)/(|y+1|)})