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Simplifying ln(7x + 14) = ln(5x + 20) Reorder the terms: ln(14 + 7x) = ln(5x + 20) (14 * ln + 7x * ln) = ln(5x + 20) (14ln + 7lnx) = ln(5x + 20) Reorder the terms: 14ln + 7lnx = ln(20 + 5x) 14ln + 7lnx = (20 * ln + 5x * ln) 14ln + 7lnx = (20ln + 5lnx) Solving 14ln + 7lnx = 20ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-20ln' to each side of the equation. 14ln + -20ln + 7lnx = 20ln + -20ln + 5lnx Combine like terms: 14ln + -20ln = -6ln -6ln + 7lnx = 20ln + -20ln + 5lnx Combine like terms: 20ln + -20ln = 0 -6ln + 7lnx = 0 + 5lnx -6ln + 7lnx = 5lnx Add '-5lnx' to each side of the equation. -6ln + 7lnx + -5lnx = 5lnx + -5lnx Combine like terms: 7lnx + -5lnx = 2lnx -6ln + 2lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -6ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-3 + x) = 0 Ignore the factor 2.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 '(-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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