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Simplifying ln(4x + 2) = 3ln(4x + -2) Reorder the terms: ln(2 + 4x) = 3ln(4x + -2) (2 * ln + 4x * ln) = 3ln(4x + -2) (2ln + 4lnx) = 3ln(4x + -2) Reorder the terms: 2ln + 4lnx = 3ln(-2 + 4x) 2ln + 4lnx = (-2 * 3ln + 4x * 3ln) 2ln + 4lnx = (-6ln + 12lnx) Solving 2ln + 4lnx = -6ln + 12lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '6ln' to each side of the equation. 2ln + 6ln + 4lnx = -6ln + 6ln + 12lnx Combine like terms: 2ln + 6ln = 8ln 8ln + 4lnx = -6ln + 6ln + 12lnx Combine like terms: -6ln + 6ln = 0 8ln + 4lnx = 0 + 12lnx 8ln + 4lnx = 12lnx Add '-12lnx' to each side of the equation. 8ln + 4lnx + -12lnx = 12lnx + -12lnx Combine like terms: 4lnx + -12lnx = -8lnx 8ln + -8lnx = 12lnx + -12lnx Combine like terms: 12lnx + -12lnx = 0 8ln + -8lnx = 0 Factor out the Greatest Common Factor (GCF), '8ln'. 8ln(1 + -1x) = 0 Ignore the factor 8.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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