ln(x+6)=ln(x-2)-1

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Solution for ln(x+6)=ln(x-2)-1 equation: 


Simplifying
ln(x + 6) = ln(x + -2) + -1

Reorder the terms:
ln(6 + x) = ln(x + -2) + -1
(6 * ln + x * ln) = ln(x + -2) + -1
(6ln + lnx) = ln(x + -2) + -1

Reorder the terms:
6ln + lnx = ln(-2 + x) + -1
6ln + lnx = (-2 * ln + x * ln) + -1
6ln + lnx = (-2ln + lnx) + -1

Reorder the terms:
6ln + lnx = -1 + -2ln + lnx

Add '-1lnx' to each side of the equation.
6ln + lnx + -1lnx = -1 + -2ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
6ln + 0 = -1 + -2ln + lnx + -1lnx
6ln = -1 + -2ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
6ln = -1 + -2ln + 0
6ln = -1 + -2ln

Solving
6ln = -1 + -2ln

Solving for variable 'l'.

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

Add '2ln' to each side of the equation.
6ln + 2ln = -1 + -2ln + 2ln

Combine like terms: 6ln + 2ln = 8ln
8ln = -1 + -2ln + 2ln

Combine like terms: -2ln + 2ln = 0
8ln = -1 + 0
8ln = -1

Divide each side by '8n'.
l = -0.125n-1

Simplifying
l = -0.125n-1

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