ln(x+2)=ln(x-4)+5

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Solution for ln(x+2)=ln(x-4)+5 equation: 


Simplifying
ln(x + 2) = ln(x + -4) + 5

Reorder the terms:
ln(2 + x) = ln(x + -4) + 5
(2 * ln + x * ln) = ln(x + -4) + 5
(2ln + lnx) = ln(x + -4) + 5

Reorder the terms:
2ln + lnx = ln(-4 + x) + 5
2ln + lnx = (-4 * ln + x * ln) + 5
2ln + lnx = (-4ln + lnx) + 5

Reorder the terms:
2ln + lnx = 5 + -4ln + lnx

Add '-1lnx' to each side of the equation.
2ln + lnx + -1lnx = 5 + -4ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
2ln + 0 = 5 + -4ln + lnx + -1lnx
2ln = 5 + -4ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
2ln = 5 + -4ln + 0
2ln = 5 + -4ln

Solving
2ln = 5 + -4ln

Solving for variable 'l'.

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

Add '4ln' to each side of the equation.
2ln + 4ln = 5 + -4ln + 4ln

Combine like terms: 2ln + 4ln = 6ln
6ln = 5 + -4ln + 4ln

Combine like terms: -4ln + 4ln = 0
6ln = 5 + 0
6ln = 5

Divide each side by '6n'.
l = 0.8333333333n-1

Simplifying
l = 0.8333333333n-1

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