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Simplifying ln(3x + -7) = ln(4x + -12) Reorder the terms: ln(-7 + 3x) = ln(4x + -12) (-7 * ln + 3x * ln) = ln(4x + -12) (-7ln + 3lnx) = ln(4x + -12) Reorder the terms: -7ln + 3lnx = ln(-12 + 4x) -7ln + 3lnx = (-12 * ln + 4x * ln) -7ln + 3lnx = (-12ln + 4lnx) Solving -7ln + 3lnx = -12ln + 4lnx 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. -7ln + 12ln + 3lnx = -12ln + 12ln + 4lnx Combine like terms: -7ln + 12ln = 5ln 5ln + 3lnx = -12ln + 12ln + 4lnx Combine like terms: -12ln + 12ln = 0 5ln + 3lnx = 0 + 4lnx 5ln + 3lnx = 4lnx Add '-4lnx' to each side of the equation. 5ln + 3lnx + -4lnx = 4lnx + -4lnx Combine like terms: 3lnx + -4lnx = -1lnx 5ln + -1lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 5ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(5 + -1x) = 0Subproblem 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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