ln(x+6)-ln(x+1)=5

Solution for ln(x+6)-ln(x+1)=5 equation:

Simplifying
ln(x + 6) + -1ln(x + 1) = 5

Reorder the terms:
ln(6 + x) + -1ln(x + 1) = 5
(6 * ln + x * ln) + -1ln(x + 1) = 5
(6ln + lnx) + -1ln(x + 1) = 5

Reorder the terms:
6ln + lnx + -1ln(1 + x) = 5
6ln + lnx + (1 * -1ln + x * -1ln) = 5
6ln + lnx + (-1ln + -1lnx) = 5

Reorder the terms:
6ln + -1ln + lnx + -1lnx = 5

Combine like terms: 6ln + -1ln = 5ln
5ln + lnx + -1lnx = 5

Combine like terms: lnx + -1lnx = 0
5ln + 0 = 5
5ln = 5

Solving
5ln = 5

Solving for variable 'l'.

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

Divide each side by '5n'.
l = n-1

Simplifying
l = n-1