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Simplifying ln(7x + 3) = ln(2x + -17) Reorder the terms: ln(3 + 7x) = ln(2x + -17) (3 * ln + 7x * ln) = ln(2x + -17) (3ln + 7lnx) = ln(2x + -17) Reorder the terms: 3ln + 7lnx = ln(-17 + 2x) 3ln + 7lnx = (-17 * ln + 2x * ln) 3ln + 7lnx = (-17ln + 2lnx) Solving 3ln + 7lnx = -17ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '17ln' to each side of the equation. 3ln + 17ln + 7lnx = -17ln + 17ln + 2lnx Combine like terms: 3ln + 17ln = 20ln 20ln + 7lnx = -17ln + 17ln + 2lnx Combine like terms: -17ln + 17ln = 0 20ln + 7lnx = 0 + 2lnx 20ln + 7lnx = 2lnx Add '-2lnx' to each side of the equation. 20ln + 7lnx + -2lnx = 2lnx + -2lnx Combine like terms: 7lnx + -2lnx = 5lnx 20ln + 5lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 20ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), '5ln'. 5ln(4 + x) = 0 Ignore the factor 5.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 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Add '-1x' to each side of the equation. x + -1x = -4 + -1x Combine like terms: x + -1x = 0 0 = -4 + -1x Simplifying 0 = -4 + -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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