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Simplifying ln(x + 4) + ln(2x + -1) = 2lnx Reorder the terms: ln(4 + x) + ln(2x + -1) = 2lnx (4 * ln + x * ln) + ln(2x + -1) = 2lnx (4ln + lnx) + ln(2x + -1) = 2lnx Reorder the terms: 4ln + lnx + ln(-1 + 2x) = 2lnx 4ln + lnx + (-1 * ln + 2x * ln) = 2lnx 4ln + lnx + (-1ln + 2lnx) = 2lnx Reorder the terms: 4ln + -1ln + lnx + 2lnx = 2lnx Combine like terms: 4ln + -1ln = 3ln 3ln + lnx + 2lnx = 2lnx Combine like terms: lnx + 2lnx = 3lnx 3ln + 3lnx = 2lnx Solving 3ln + 3lnx = 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. 3ln + 3lnx + -2lnx = 2lnx + -2lnx Combine like terms: 3lnx + -2lnx = 1lnx 3ln + 1lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 3ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(3 + x) = 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 '(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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