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Simplifying ln(x + 4) + ln(2x + 3) = ln(1 + -2x) Reorder the terms: ln(4 + x) + ln(2x + 3) = ln(1 + -2x) (4 * ln + x * ln) + ln(2x + 3) = ln(1 + -2x) (4ln + lnx) + ln(2x + 3) = ln(1 + -2x) Reorder the terms: 4ln + lnx + ln(3 + 2x) = ln(1 + -2x) 4ln + lnx + (3 * ln + 2x * ln) = ln(1 + -2x) 4ln + lnx + (3ln + 2lnx) = ln(1 + -2x) Reorder the terms: 4ln + 3ln + lnx + 2lnx = ln(1 + -2x) Combine like terms: 4ln + 3ln = 7ln 7ln + lnx + 2lnx = ln(1 + -2x) Combine like terms: lnx + 2lnx = 3lnx 7ln + 3lnx = ln(1 + -2x) 7ln + 3lnx = (1 * ln + -2x * ln) 7ln + 3lnx = (1ln + -2lnx) Solving 7ln + 3lnx = 1ln + -2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. 7ln + -1ln + 3lnx = 1ln + -1ln + -2lnx Combine like terms: 7ln + -1ln = 6ln 6ln + 3lnx = 1ln + -1ln + -2lnx Combine like terms: 1ln + -1ln = 0 6ln + 3lnx = 0 + -2lnx 6ln + 3lnx = -2lnx Add '2lnx' to each side of the equation. 6ln + 3lnx + 2lnx = -2lnx + 2lnx Combine like terms: 3lnx + 2lnx = 5lnx 6ln + 5lnx = -2lnx + 2lnx Combine like terms: -2lnx + 2lnx = 0 6ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(6 + 5x) = 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 '(6 + 5x)' equal to zero and attempt to solve: Simplifying 6 + 5x = 0 Solving 6 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5x = 0 + -6 5x = 0 + -6 Combine like terms: 0 + -6 = -6 5x = -6 Add '-5x' to each side of the equation. 5x + -5x = -6 + -5x Combine like terms: 5x + -5x = 0 0 = -6 + -5x Simplifying 0 = -6 + -5x 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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