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