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Simplifying ln(7x + 2) = ln(5x + -14) Reorder the terms: ln(2 + 7x) = ln(5x + -14) (2 * ln + 7x * ln) = ln(5x + -14) (2ln + 7lnx) = ln(5x + -14) Reorder the terms: 2ln + 7lnx = ln(-14 + 5x) 2ln + 7lnx = (-14 * ln + 5x * ln) 2ln + 7lnx = (-14ln + 5lnx) Solving 2ln + 7lnx = -14ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '14ln' to each side of the equation. 2ln + 14ln + 7lnx = -14ln + 14ln + 5lnx Combine like terms: 2ln + 14ln = 16ln 16ln + 7lnx = -14ln + 14ln + 5lnx Combine like terms: -14ln + 14ln = 0 16ln + 7lnx = 0 + 5lnx 16ln + 7lnx = 5lnx Add '-5lnx' to each side of the equation. 16ln + 7lnx + -5lnx = 5lnx + -5lnx Combine like terms: 7lnx + -5lnx = 2lnx 16ln + 2lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 16ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(8 + 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 '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Add '-1x' to each side of the equation. x + -1x = -8 + -1x Combine like terms: x + -1x = 0 0 = -8 + -1x Simplifying 0 = -8 + -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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