Solve for x exactly lnx3lnx2ln2Solutionlnx3 lnx 2ln2 lnx

Solve for x exactly: ln(x+3)-lnx=2ln2

Solution

ln(x+3) - lnx = 2ln2

==> ln[(x +3)/x] = 2ln2      since lna - lnb = ln(a/b)

==> ln[(x +3)/x] = ln2²    since alnb = lnb^a

apply anti log on both sides

==> (x +3)/x = 2²

==> x+3 = 4x

==> 3x = 3

==> x = 1

Hence x = 1