What is 2/5 ln|4w+1|+3/5 ln|w-1| ?

The solution to 2/5 ln|4w+1|+3/5 ln|w-1| is ln(|4w+1|^{2/5}|w-1|^{3/5})

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simplify 2/5 ln|4w+1|+3/5 ln|w-1|

simplify

\frac{2}{5} ln ∣ 4 w + 1 ∣ + \frac{3}{5} ln ∣ w - 1 ∣

ln (∣ 4 w + 1 ∣^{\frac{2}{5}} ∣ w - 1 ∣^{\frac{3}{5}})

Solution steps

\frac{2}{5} ln ∣ 4 w + 1 ∣ + \frac{3}{5} ln ∣ w - 1 ∣

Apply log rule:

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

\frac{2}{5} ln ∣ 4 w + 1 ∣ = ln (∣ 4 w + 1 ∣^{\frac{2}{5}})

= ln (∣ 4 w + 1 ∣^{\frac{2}{5}}) + \frac{3}{5} ln ∣ w - 1 ∣

Apply log rule:

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

\frac{3}{5} ln ∣ w - 1 ∣ = ln (∣ w - 1 ∣^{\frac{3}{5}})

= ln (∣ 4 w + 1 ∣^{\frac{2}{5}}) + ln (∣ w - 1 ∣^{\frac{3}{5}})

Apply log rule:

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

ln (∣ 4 w + 1 ∣^{\frac{2}{5}}) + ln (∣ w - 1 ∣^{\frac{3}{5}}) = ln (∣ w - 1 ∣^{\frac{3}{5}} ∣ 4 w + 1 ∣^{\frac{2}{5}})

= ln (∣ 4 w + 1 ∣^{\frac{2}{5}} ∣ w - 1 ∣^{\frac{3}{5}})

ln (\frac{0.019}{0.005})

(\frac{- x}{x + y}) + (ln (x^{2} + y^{2}) - 2 ln (x))

- lo g_{10} (4.21 \cdot 1 0^{- 5})

- lo g_{10} (3.7 \cdot 1 0^{- 7})

ln (\frac{210 e ^{x}}{4.1 + 1.2 e ^{x}})

What is 2/5 ln|4w+1|+3/5 ln|w-1| ?
The solution to 2/5 ln|4w+1|+3/5 ln|w-1| is ln(|4w+1|^{2/5}|w-1|^{3/5})