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Simplifying ln(6x + 18) = ln(5x + 8) Reorder the terms: ln(18 + 6x) = ln(5x + 8) (18 * ln + 6x * ln) = ln(5x + 8) (18ln + 6lnx) = ln(5x + 8) Reorder the terms: 18ln + 6lnx = ln(8 + 5x) 18ln + 6lnx = (8 * ln + 5x * ln) 18ln + 6lnx = (8ln + 5lnx) Solving 18ln + 6lnx = 8ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. 18ln + -8ln + 6lnx = 8ln + -8ln + 5lnx Combine like terms: 18ln + -8ln = 10ln 10ln + 6lnx = 8ln + -8ln + 5lnx Combine like terms: 8ln + -8ln = 0 10ln + 6lnx = 0 + 5lnx 10ln + 6lnx = 5lnx Add '-5lnx' to each side of the equation. 10ln + 6lnx + -5lnx = 5lnx + -5lnx Combine like terms: 6lnx + -5lnx = 1lnx 10ln + 1lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 10ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(10 + x) = 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 '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Add '-1x' to each side of the equation. x + -1x = -10 + -1x Combine like terms: x + -1x = 0 0 = -10 + -1x Simplifying 0 = -10 + -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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