ln(x+6)=4+ln(x-6)

Solution for ln(x+6)=4+ln(x-6) equation:

Simplifying
ln(x + 6) = 4 + ln(x + -6)

Reorder the terms:
ln(6 + x) = 4 + ln(x + -6)
(6 * ln + x * ln) = 4 + ln(x + -6)
(6ln + lnx) = 4 + ln(x + -6)

Reorder the terms:
6ln + lnx = 4 + ln(-6 + x)
6ln + lnx = 4 + (-6 * ln + x * ln)
6ln + lnx = 4 + (-6ln + lnx)

Add '-1lnx' to each side of the equation.
6ln + lnx + -1lnx = 4 + -6ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
6ln + 0 = 4 + -6ln + lnx + -1lnx
6ln = 4 + -6ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
6ln = 4 + -6ln + 0
6ln = 4 + -6ln

Solving
6ln = 4 + -6ln

Solving for variable 'l'.

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

Add '6ln' to each side of the equation.
6ln + 6ln = 4 + -6ln + 6ln

Combine like terms: 6ln + 6ln = 12ln
12ln = 4 + -6ln + 6ln

Combine like terms: -6ln + 6ln = 0
12ln = 4 + 0
12ln = 4

Divide each side by '12n'.
l = 0.3333333333n-1

Simplifying
l = 0.3333333333n-1