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Simplifying ln(2x + 3) + ln(-5x + 4) = ln(-7 + 2) Reorder the terms: ln(3 + 2x) + ln(-5x + 4) = ln(-7 + 2) (3 * ln + 2x * ln) + ln(-5x + 4) = ln(-7 + 2) (3ln + 2lnx) + ln(-5x + 4) = ln(-7 + 2) Reorder the terms: 3ln + 2lnx + ln(4 + -5x) = ln(-7 + 2) 3ln + 2lnx + (4 * ln + -5x * ln) = ln(-7 + 2) 3ln + 2lnx + (4ln + -5lnx) = ln(-7 + 2) Reorder the terms: 3ln + 4ln + 2lnx + -5lnx = ln(-7 + 2) Combine like terms: 3ln + 4ln = 7ln 7ln + 2lnx + -5lnx = ln(-7 + 2) Combine like terms: 2lnx + -5lnx = -3lnx 7ln + -3lnx = ln(-7 + 2) Combine like terms: -7 + 2 = -5 7ln + -3lnx = ln(-5) Reorder the terms for easier multiplication: 7ln + -3lnx = -5ln Solving 7ln + -3lnx = -5ln 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. 7ln + 5ln + -3lnx = -5ln + 5ln Combine like terms: 7ln + 5ln = 12ln 12ln + -3lnx = -5ln + 5ln Combine like terms: -5ln + 5ln = 0 12ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(4 + -1x) = 0 Ignore the factor 3.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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + x 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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