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

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

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simplify 1/5 (4ln(x+4)+ln(x-1))+c

simplify

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

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

Solution steps

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

Apply log rule:

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

4 ln (x + 4) = ln ((x + 4)^{4})

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

Apply log rule:

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

ln ((x + 4)^{4}) + ln (x - 1) = ln ((x + 4)^{4} (x - 1))

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

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

ln (\frac{0.003789035}{0.001129995})

ln (\frac{6}{16})

ln (\frac{e ^{x + 2 y}}{1 - ( e ^{x + 2 y} )})

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