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