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