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Simplifying ln(5x + 18) = ln(2x + 6) Reorder the terms: ln(18 + 5x) = ln(2x + 6) (18 * ln + 5x * ln) = ln(2x + 6) (18ln + 5lnx) = ln(2x + 6) Reorder the terms: 18ln + 5lnx = ln(6 + 2x) 18ln + 5lnx = (6 * ln + 2x * ln) 18ln + 5lnx = (6ln + 2lnx) Solving 18ln + 5lnx = 6ln + 2lnx 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. 18ln + -6ln + 5lnx = 6ln + -6ln + 2lnx Combine like terms: 18ln + -6ln = 12ln 12ln + 5lnx = 6ln + -6ln + 2lnx Combine like terms: 6ln + -6ln = 0 12ln + 5lnx = 0 + 2lnx 12ln + 5lnx = 2lnx Add '-2lnx' to each side of the equation. 12ln + 5lnx + -2lnx = 2lnx + -2lnx Combine like terms: 5lnx + -2lnx = 3lnx 12ln + 3lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 12ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(4 + x) = 0 Ignore the factor 3.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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Add '-1x' to each side of the equation. x + -1x = -4 + -1x Combine like terms: x + -1x = 0 0 = -4 + -1x Simplifying 0 = -4 + -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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