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Simplifying ln(x) = ln(3x + 2) Multiply ln * x lnx = ln(3x + 2) Reorder the terms: lnx = ln(2 + 3x) lnx = (2 * ln + 3x * ln) lnx = (2ln + 3lnx) Solving lnx = 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. -2ln + lnx = 2ln + -2ln + 3lnx Combine like terms: 2ln + -2ln = 0 -2ln + lnx = 0 + 3lnx -2ln + lnx = 3lnx Add '-3lnx' to each side of the equation. -2ln + lnx + -3lnx = 3lnx + -3lnx Combine like terms: lnx + -3lnx = -2lnx -2ln + -2lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -2ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(1 + x) = 0 Ignore the factor -2.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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