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Simplifying ln(3) + ln(2x + -1) = ln(4) + ln(x + 1) Reorder the terms for easier multiplication: 3ln + ln(2x + -1) = ln(4) + ln(x + 1) Reorder the terms: 3ln + ln(-1 + 2x) = ln(4) + ln(x + 1) 3ln + (-1 * ln + 2x * ln) = ln(4) + ln(x + 1) 3ln + (-1ln + 2lnx) = ln(4) + ln(x + 1) Combine like terms: 3ln + -1ln = 2ln 2ln + 2lnx = ln(4) + ln(x + 1) Reorder the terms for easier multiplication: 2ln + 2lnx = 4ln + ln(x + 1) Reorder the terms: 2ln + 2lnx = 4ln + ln(1 + x) 2ln + 2lnx = 4ln + (1 * ln + x * ln) 2ln + 2lnx = 4ln + (1ln + lnx) Combine like terms: 4ln + 1ln = 5ln 2ln + 2lnx = 5ln + lnx Solving 2ln + 2lnx = 5ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. 2ln + -5ln + 2lnx = 5ln + -5ln + lnx Combine like terms: 2ln + -5ln = -3ln -3ln + 2lnx = 5ln + -5ln + lnx Combine like terms: 5ln + -5ln = 0 -3ln + 2lnx = 0 + lnx -3ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -3ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -3ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 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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