What is ln|x|+1/5 ln|1+5u^3| ?

The solution to ln|x|+1/5 ln|1+5u^3| is ln(|x||1+5u^3|^{1/5})

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simplify ln|x|+1/5 ln|1+5u^3|

simplify

ln ∣ x ∣ + \frac{1}{5} ln 1 + 5 u^{3}

ln (∣ x ∣ 1 + 5 u^{3}^{\frac{1}{5}})

Solution steps

ln ∣ x ∣ + \frac{1}{5} ln 1 + 5 u^{3}

Apply log rule:

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

\frac{1}{5} ln 5 u^{3} + 1 = ln (5 u^{3} + 1^{\frac{1}{5}})

= ln ∣ x ∣ + ln (5 u^{3} + 1^{\frac{1}{5}})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln ∣ x ∣ + ln (1 + 5 u^{3}^{\frac{1}{5}}) = ln (∣ x ∣ 5 u^{3} + 1^{\frac{1}{5}})

= ln (∣ x ∣ 1 + 5 u^{3}^{\frac{1}{5}})

3 ln (x + 1) + 3 ln (x - 1)

ln (a) - ln (s^{2} + 4)

ln (\frac{- 78}{- 80})

ln (\frac{3857 - 8626449}{2500})

ln (\frac{3 e ^{2}}{2})

What is ln|x|+1/5 ln|1+5u^3| ?
The solution to ln|x|+1/5 ln|1+5u^3| is ln(|x||1+5u^3|^{1/5})