2lnx-2lnx+3ln=5lnx-lnx+2ln

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Solution for 2lnx-2lnx+3ln=5lnx-lnx+2ln equation:


Simplifying
2lnx + -2lnx + 3ln = 5lnx + -1lnx + 2ln

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

Combine like terms: 2lnx + -2lnx = 0
3ln + 0 = 5lnx + -1lnx + 2ln
3ln = 5lnx + -1lnx + 2ln

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

Combine like terms: 5lnx + -1lnx = 4lnx
3ln = 2ln + 4lnx

Solving
3ln = 2ln + 4lnx

Solving for variable 'l'.

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

Add '-2ln' to each side of the equation.
3ln + -2ln = 2ln + -2ln + 4lnx

Combine like terms: 3ln + -2ln = 1ln
1ln = 2ln + -2ln + 4lnx

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

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + -4x) = 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 '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Add '4x' to each side of the equation. -4x + 4x = -1 + 4x Combine like terms: -4x + 4x = 0 0 = -1 + 4x Simplifying 0 = -1 + 4x 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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