ln(x-6)+(x+1)=ln(x-15)

Solution for ln(x-6)+(x+1)=ln(x-15) equation:

Simplifying
ln(x + -6) + (x + 1) = ln(x + -15)

Reorder the terms:
ln(-6 + x) + (x + 1) = ln(x + -15)
(-6 * ln + x * ln) + (x + 1) = ln(x + -15)
(-6ln + lnx) + (x + 1) = ln(x + -15)

Reorder the terms:
-6ln + lnx + (1 + x) = ln(x + -15)

Remove parenthesis around (1 + x)
-6ln + lnx + 1 + x = ln(x + -15)

Reorder the terms:
1 + -6ln + lnx + x = ln(x + -15)

Reorder the terms:
1 + -6ln + lnx + x = ln(-15 + x)
1 + -6ln + lnx + x = (-15 * ln + x * ln)
1 + -6ln + lnx + x = (-15ln + lnx)

Add '-1lnx' to each side of the equation.
1 + -6ln + lnx + -1lnx + x = -15ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
1 + -6ln + 0 + x = -15ln + lnx + -1lnx
1 + -6ln + x = -15ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
1 + -6ln + x = -15ln + 0
1 + -6ln + x = -15ln

Solving
1 + -6ln + x = -15ln

Solving for variable 'l'.

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

Add '15ln' to each side of the equation.
1 + -6ln + 15ln + x = -15ln + 15ln

Combine like terms: -6ln + 15ln = 9ln
1 + 9ln + x = -15ln + 15ln

Combine like terms: -15ln + 15ln = 0
1 + 9ln + x = 0

Add '-1' to each side of the equation.
1 + 9ln + -1 + x = 0 + -1

Reorder the terms:
1 + -1 + 9ln + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9ln + x = 0 + -1
9ln + x = 0 + -1

Combine like terms: 0 + -1 = -1
9ln + x = -1

Add '-1x' to each side of the equation.
9ln + x + -1x = -1 + -1x

Combine like terms: x + -1x = 0
9ln + 0 = -1 + -1x
9ln = -1 + -1x

Divide each side by '9n'.
l = -0.1111111111n-1 + -0.1111111111n-1x

Simplifying
l = -0.1111111111n-1 + -0.1111111111n-1x