ln(2x+3)=ln(5x-6)

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Solution for ln(2x+3)=ln(5x-6) equation:


Simplifying
ln(2x + 3) = ln(5x + -6)

Reorder the terms:
ln(3 + 2x) = ln(5x + -6)
(3 * ln + 2x * ln) = ln(5x + -6)
(3ln + 2lnx) = ln(5x + -6)

Reorder the terms:
3ln + 2lnx = ln(-6 + 5x)
3ln + 2lnx = (-6 * ln + 5x * ln)
3ln + 2lnx = (-6ln + 5lnx)

Solving
3ln + 2lnx = -6ln + 5lnx

Solving for variable 'l'.

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

Add '6ln' to each side of the equation.
3ln + 6ln + 2lnx = -6ln + 6ln + 5lnx

Combine like terms: 3ln + 6ln = 9ln
9ln + 2lnx = -6ln + 6ln + 5lnx

Combine like terms: -6ln + 6ln = 0
9ln + 2lnx = 0 + 5lnx
9ln + 2lnx = 5lnx

Add '-5lnx' to each side of the equation.
9ln + 2lnx + -5lnx = 5lnx + -5lnx

Combine like terms: 2lnx + -5lnx = -3lnx
9ln + -3lnx = 5lnx + -5lnx

Combine like terms: 5lnx + -5lnx = 0
9ln + -3lnx = 0

Factor out the Greatest Common Factor (GCF), '3ln'.
3ln(3 + -1x) = 0

Ignore the factor 3.

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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + 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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