ln(x+3)=ln(x-3)+1.5

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Solution for ln(x+3)=ln(x-3)+1.5 equation: 


Simplifying
ln(x + 3) = ln(x + -3) + 1.5

Reorder the terms:
ln(3 + x) = ln(x + -3) + 1.5
(3 * ln + x * ln) = ln(x + -3) + 1.5
(3ln + lnx) = ln(x + -3) + 1.5

Reorder the terms:
3ln + lnx = ln(-3 + x) + 1.5
3ln + lnx = (-3 * ln + x * ln) + 1.5
3ln + lnx = (-3ln + lnx) + 1.5

Reorder the terms:
3ln + lnx = 1.5 + -3ln + lnx

Add '-1lnx' to each side of the equation.
3ln + lnx + -1lnx = 1.5 + -3ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
3ln + 0 = 1.5 + -3ln + lnx + -1lnx
3ln = 1.5 + -3ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
3ln = 1.5 + -3ln + 0
3ln = 1.5 + -3ln

Solving
3ln = 1.5 + -3ln

Solving for variable 'l'.

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

Add '3ln' to each side of the equation.
3ln + 3ln = 1.5 + -3ln + 3ln

Combine like terms: 3ln + 3ln = 6ln
6ln = 1.5 + -3ln + 3ln

Combine like terms: -3ln + 3ln = 0
6ln = 1.5 + 0
6ln = 1.5

Divide each side by '6n'.
l = 0.25n-1

Simplifying
l = 0.25n-1

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