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Simplifying ln(3x + 1) + ln(x + 2) = ln(6x + 4) Reorder the terms: ln(1 + 3x) + ln(x + 2) = ln(6x + 4) (1 * ln + 3x * ln) + ln(x + 2) = ln(6x + 4) (1ln + 3lnx) + ln(x + 2) = ln(6x + 4) Reorder the terms: 1ln + 3lnx + ln(2 + x) = ln(6x + 4) 1ln + 3lnx + (2 * ln + x * ln) = ln(6x + 4) 1ln + 3lnx + (2ln + lnx) = ln(6x + 4) Reorder the terms: 1ln + 2ln + 3lnx + lnx = ln(6x + 4) Combine like terms: 1ln + 2ln = 3ln 3ln + 3lnx + lnx = ln(6x + 4) Combine like terms: 3lnx + lnx = 4lnx 3ln + 4lnx = ln(6x + 4) Reorder the terms: 3ln + 4lnx = ln(4 + 6x) 3ln + 4lnx = (4 * ln + 6x * ln) 3ln + 4lnx = (4ln + 6lnx) Solving 3ln + 4lnx = 4ln + 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. 3ln + -4ln + 4lnx = 4ln + -4ln + 6lnx Combine like terms: 3ln + -4ln = -1ln -1ln + 4lnx = 4ln + -4ln + 6lnx Combine like terms: 4ln + -4ln = 0 -1ln + 4lnx = 0 + 6lnx -1ln + 4lnx = 6lnx Add '-6lnx' to each side of the equation. -1ln + 4lnx + -6lnx = 6lnx + -6lnx Combine like terms: 4lnx + -6lnx = -2lnx -1ln + -2lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 -1ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(1 + 2x) = 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 '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -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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