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