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

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


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

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

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

Solving
2ln + 3lnx = 1ln + 2lnx

Solving for variable 'l'.

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

Add '-1ln' to each side of the equation.
2ln + -1ln + 3lnx = 1ln + -1ln + 2lnx

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

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

Add '-2lnx' to each side of the equation.
1ln + 3lnx + -2lnx = 2lnx + -2lnx

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

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

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