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

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


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

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

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

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

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

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

Reorder the terms:
-5ln + 3lnx = 2ln(-2 + 2x)
-5ln + 3lnx = (-2 * 2ln + 2x * 2ln)
-5ln + 3lnx = (-4ln + 4lnx)

Solving
-5ln + 3lnx = -4ln + 4lnx

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.
-5ln + 4ln + 3lnx = -4ln + 4ln + 4lnx

Combine like terms: -5ln + 4ln = -1ln
-1ln + 3lnx = -4ln + 4ln + 4lnx

Combine like terms: -4ln + 4ln = 0
-1ln + 3lnx = 0 + 4lnx
-1ln + 3lnx = 4lnx

Add '-4lnx' to each side of the equation.
-1ln + 3lnx + -4lnx = 4lnx + -4lnx

Combine like terms: 3lnx + -4lnx = -1lnx
-1ln + -1lnx = 4lnx + -4lnx

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

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(1 + x) = 0

Ignore the factor -1.

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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -1x 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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