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Simplifying ln(3x + -24) = ln(1 + -2x) Reorder the terms: ln(-24 + 3x) = ln(1 + -2x) (-24 * ln + 3x * ln) = ln(1 + -2x) (-24ln + 3lnx) = ln(1 + -2x) -24ln + 3lnx = (1 * ln + -2x * ln) -24ln + 3lnx = (1ln + -2lnx) Solving -24ln + 3lnx = 1ln + -2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. -24ln + -1ln + 3lnx = 1ln + -1ln + -2lnx Combine like terms: -24ln + -1ln = -25ln -25ln + 3lnx = 1ln + -1ln + -2lnx Combine like terms: 1ln + -1ln = 0 -25ln + 3lnx = 0 + -2lnx -25ln + 3lnx = -2lnx Add '2lnx' to each side of the equation. -25ln + 3lnx + 2lnx = -2lnx + 2lnx Combine like terms: 3lnx + 2lnx = 5lnx -25ln + 5lnx = -2lnx + 2lnx Combine like terms: -2lnx + 2lnx = 0 -25ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), '5ln'. 5ln(-5 + x) = 0 Ignore the factor 5.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 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 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 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Add '-1x' to each side of the equation. x + -1x = 5 + -1x Combine like terms: x + -1x = 0 0 = 5 + -1x Simplifying 0 = 5 + -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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