ln(x-1)-ln(x-3)=ln(2x-5)

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Solution for ln(x-1)-ln(x-3)=ln(2x-5) equation:


Simplifying
ln(x + -1) + -1ln(x + -3) = ln(2x + -5)

Reorder the terms:
ln(-1 + x) + -1ln(x + -3) = ln(2x + -5)
(-1 * ln + x * ln) + -1ln(x + -3) = ln(2x + -5)
(-1ln + lnx) + -1ln(x + -3) = ln(2x + -5)

Reorder the terms:
-1ln + lnx + -1ln(-3 + x) = ln(2x + -5)
-1ln + lnx + (-3 * -1ln + x * -1ln) = ln(2x + -5)
-1ln + lnx + (3ln + -1lnx) = ln(2x + -5)

Reorder the terms:
-1ln + 3ln + lnx + -1lnx = ln(2x + -5)

Combine like terms: -1ln + 3ln = 2ln
2ln + lnx + -1lnx = ln(2x + -5)

Combine like terms: lnx + -1lnx = 0
2ln + 0 = ln(2x + -5)
2ln = ln(2x + -5)

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

Solving
2ln = -5ln + 2lnx

Solving for variable 'l'.

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

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

Combine like terms: 2ln + 5ln = 7ln
7ln = -5ln + 5ln + 2lnx

Combine like terms: -5ln + 5ln = 0
7ln = 0 + 2lnx
7ln = 2lnx

Add '-2lnx' to each side of the equation.
7ln + -2lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
7ln + -2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(7 + -2x) = 0

Subproblem 1

Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Add '2x' to each side of the equation. -2x + 2x = -7 + 2x Combine like terms: -2x + 2x = 0 0 = -7 + 2x Simplifying 0 = -7 + 2x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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