ln(2z+1)-ln(z+1)=2

Solution for ln(2z+1)-ln(z+1)=2 equation:

Simplifying
ln(2z + 1) + -1ln(z + 1) = 2

Reorder the terms:
ln(1 + 2z) + -1ln(z + 1) = 2
(1 * ln + 2z * ln) + -1ln(z + 1) = 2
(1ln + 2lnz) + -1ln(z + 1) = 2

Reorder the terms:
1ln + 2lnz + -1ln(1 + z) = 2
1ln + 2lnz + (1 * -1ln + z * -1ln) = 2
1ln + 2lnz + (-1ln + -1lnz) = 2

Reorder the terms:
1ln + -1ln + 2lnz + -1lnz = 2

Combine like terms: 1ln + -1ln = 0
0 + 2lnz + -1lnz = 2
2lnz + -1lnz = 2

Combine like terms: 2lnz + -1lnz = 1lnz
1lnz = 2

Solving
1lnz = 2

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Divide each side by '1nz'.
l = 2n-1z-1

Simplifying
l = 2n-1z-1