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Simplifying ln(3x + 1) = ln(5x + -7) Reorder the terms: ln(1 + 3x) = ln(5x + -7) (1 * ln + 3x * ln) = ln(5x + -7) (1ln + 3lnx) = ln(5x + -7) Reorder the terms: 1ln + 3lnx = ln(-7 + 5x) 1ln + 3lnx = (-7 * ln + 5x * ln) 1ln + 3lnx = (-7ln + 5lnx) Solving 1ln + 3lnx = -7ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '7ln' to each side of the equation. 1ln + 7ln + 3lnx = -7ln + 7ln + 5lnx Combine like terms: 1ln + 7ln = 8ln 8ln + 3lnx = -7ln + 7ln + 5lnx Combine like terms: -7ln + 7ln = 0 8ln + 3lnx = 0 + 5lnx 8ln + 3lnx = 5lnx Add '-5lnx' to each side of the equation. 8ln + 3lnx + -5lnx = 5lnx + -5lnx Combine like terms: 3lnx + -5lnx = -2lnx 8ln + -2lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 8ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(4 + -1x) = 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 '(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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