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Simplifying ln(5x + -1) = ln(3x + 2) Reorder the terms: ln(-1 + 5x) = ln(3x + 2) (-1 * ln + 5x * ln) = ln(3x + 2) (-1ln + 5lnx) = ln(3x + 2) Reorder the terms: -1ln + 5lnx = ln(2 + 3x) -1ln + 5lnx = (2 * ln + 3x * ln) -1ln + 5lnx = (2ln + 3lnx) Solving -1ln + 5lnx = 2ln + 3lnx 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. -1ln + -2ln + 5lnx = 2ln + -2ln + 3lnx Combine like terms: -1ln + -2ln = -3ln -3ln + 5lnx = 2ln + -2ln + 3lnx Combine like terms: 2ln + -2ln = 0 -3ln + 5lnx = 0 + 3lnx -3ln + 5lnx = 3lnx Add '-3lnx' to each side of the equation. -3ln + 5lnx + -3lnx = 3lnx + -3lnx Combine like terms: 5lnx + -3lnx = 2lnx -3ln + 2lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -3ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-3 + 2x) = 0Subproblem 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 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 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 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Add '-2x' to each side of the equation. 2x + -2x = 3 + -2x Combine like terms: 2x + -2x = 0 0 = 3 + -2x Simplifying 0 = 3 + -2x 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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