ln(x-4)+(x+1)=ln(x-8)

Solution for ln(x-4)+(x+1)=ln(x-8) equation:

Simplifying
ln(x + -4) + (x + 1) = ln(x + -8)

Reorder the terms:
ln(-4 + x) + (x + 1) = ln(x + -8)
(-4 * ln + x * ln) + (x + 1) = ln(x + -8)
(-4ln + lnx) + (x + 1) = ln(x + -8)

Reorder the terms:
-4ln + lnx + (1 + x) = ln(x + -8)

Remove parenthesis around (1 + x)
-4ln + lnx + 1 + x = ln(x + -8)

Reorder the terms:
1 + -4ln + lnx + x = ln(x + -8)

Reorder the terms:
1 + -4ln + lnx + x = ln(-8 + x)
1 + -4ln + lnx + x = (-8 * ln + x * ln)
1 + -4ln + lnx + x = (-8ln + lnx)

Add '-1lnx' to each side of the equation.
1 + -4ln + lnx + -1lnx + x = -8ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
1 + -4ln + 0 + x = -8ln + lnx + -1lnx
1 + -4ln + x = -8ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
1 + -4ln + x = -8ln + 0
1 + -4ln + x = -8ln

Solving
1 + -4ln + x = -8ln

Solving for variable 'l'.

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

Add '8ln' to each side of the equation.
1 + -4ln + 8ln + x = -8ln + 8ln

Combine like terms: -4ln + 8ln = 4ln
1 + 4ln + x = -8ln + 8ln

Combine like terms: -8ln + 8ln = 0
1 + 4ln + x = 0

Add '-1' to each side of the equation.
1 + 4ln + -1 + x = 0 + -1

Reorder the terms:
1 + -1 + 4ln + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4ln + x = 0 + -1
4ln + x = 0 + -1

Combine like terms: 0 + -1 = -1
4ln + x = -1

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

Combine like terms: x + -1x = 0
4ln + 0 = -1 + -1x
4ln = -1 + -1x

Divide each side by '4n'.
l = -0.25n-1 + -0.25n-1x

Simplifying
l = -0.25n-1 + -0.25n-1x