prove both equations are equal lnabsx1 2lnabsx 3ln4 c lnx2a

prove both equations are equal

lnabs(x+1) +2lnabs(x) +3ln(4) +c = ln(x*2)abs(x+1)+c

Solution

sol:
given that...
lnabs(x+1) +2lnabs(x) +3ln(4) +c = ln(x*2)abs(x+1)+c
now fro LHS...
lnabs(x+1) +2lnabs(x) +3ln(4) +c
= abs(ln(x+1))+2abs(lnx)+3ln(4)+c
=absln(x)+absln+2abs(lnx)+3ln(4)+c
=absln(x)+0+2absln(x)+3ln(4)+c