ln(x-2)-ln(x-1)=3

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Solution for ln(x-2)-ln(x-1)=3 equation: 


Simplifying
ln(x + -2) + -1ln(x + -1) = 3

Reorder the terms:
ln(-2 + x) + -1ln(x + -1) = 3
(-2 * ln + x * ln) + -1ln(x + -1) = 3
(-2ln + lnx) + -1ln(x + -1) = 3

Reorder the terms:
-2ln + lnx + -1ln(-1 + x) = 3
-2ln + lnx + (-1 * -1ln + x * -1ln) = 3
-2ln + lnx + (1ln + -1lnx) = 3

Reorder the terms:
-2ln + 1ln + lnx + -1lnx = 3

Combine like terms: -2ln + 1ln = -1ln
-1ln + lnx + -1lnx = 3

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

Solving
-1ln = 3

Solving for variable 'l'.

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

Divide each side by '-1n'.
l = -3n-1

Simplifying
l = -3n-1

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