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

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


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

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

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

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

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

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

Reorder the terms for easier multiplication:
4ln + -1lnx = 2ln

Solving
4ln + -1lnx = 2ln

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.
4ln + -2ln + -1lnx = 2ln + -2ln

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(2 + -1x) = 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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