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Simplifying ln(5x + 18) = ln(12x + 4) Reorder the terms: ln(18 + 5x) = ln(12x + 4) (18 * ln + 5x * ln) = ln(12x + 4) (18ln + 5lnx) = ln(12x + 4) Reorder the terms: 18ln + 5lnx = ln(4 + 12x) 18ln + 5lnx = (4 * ln + 12x * ln) 18ln + 5lnx = (4ln + 12lnx) Solving 18ln + 5lnx = 4ln + 12lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. 18ln + -4ln + 5lnx = 4ln + -4ln + 12lnx Combine like terms: 18ln + -4ln = 14ln 14ln + 5lnx = 4ln + -4ln + 12lnx Combine like terms: 4ln + -4ln = 0 14ln + 5lnx = 0 + 12lnx 14ln + 5lnx = 12lnx Add '-12lnx' to each side of the equation. 14ln + 5lnx + -12lnx = 12lnx + -12lnx Combine like terms: 5lnx + -12lnx = -7lnx 14ln + -7lnx = 12lnx + -12lnx Combine like terms: 12lnx + -12lnx = 0 14ln + -7lnx = 0 Factor out the Greatest Common Factor (GCF), '7ln'. 7ln(2 + -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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + 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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