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Simplifying ln(3x + -2) = ln(5x + -12) Reorder the terms: ln(-2 + 3x) = ln(5x + -12) (-2 * ln + 3x * ln) = ln(5x + -12) (-2ln + 3lnx) = ln(5x + -12) Reorder the terms: -2ln + 3lnx = ln(-12 + 5x) -2ln + 3lnx = (-12 * ln + 5x * ln) -2ln + 3lnx = (-12ln + 5lnx) Solving -2ln + 3lnx = -12ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '12ln' to each side of the equation. -2ln + 12ln + 3lnx = -12ln + 12ln + 5lnx Combine like terms: -2ln + 12ln = 10ln 10ln + 3lnx = -12ln + 12ln + 5lnx Combine like terms: -12ln + 12ln = 0 10ln + 3lnx = 0 + 5lnx 10ln + 3lnx = 5lnx Add '-5lnx' to each side of the equation. 10ln + 3lnx + -5lnx = 5lnx + -5lnx Combine like terms: 3lnx + -5lnx = -2lnx 10ln + -2lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 10ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(5 + -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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + 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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