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Simplifying ln(x + 3) = ln(2x + -5) Reorder the terms: ln(3 + x) = ln(2x + -5) (3 * ln + x * ln) = ln(2x + -5) (3ln + lnx) = ln(2x + -5) Reorder the terms: 3ln + lnx = ln(-5 + 2x) 3ln + lnx = (-5 * ln + 2x * ln) 3ln + lnx = (-5ln + 2lnx) Solving 3ln + lnx = -5ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '5ln' to each side of the equation. 3ln + 5ln + lnx = -5ln + 5ln + 2lnx Combine like terms: 3ln + 5ln = 8ln 8ln + lnx = -5ln + 5ln + 2lnx Combine like terms: -5ln + 5ln = 0 8ln + lnx = 0 + 2lnx 8ln + lnx = 2lnx Add '-2lnx' to each side of the equation. 8ln + lnx + -2lnx = 2lnx + -2lnx Combine like terms: lnx + -2lnx = -1lnx 8ln + -1lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 8ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(8 + -1x) = 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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Add 'x' to each side of the equation. -1x + x = -8 + x Combine like terms: -1x + x = 0 0 = -8 + x Simplifying 0 = -8 + 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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