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Simplifying ln(6x + 6) = ln(5x + 2) Reorder the terms: ln(6 + 6x) = ln(5x + 2) (6 * ln + 6x * ln) = ln(5x + 2) (6ln + 6lnx) = ln(5x + 2) Reorder the terms: 6ln + 6lnx = ln(2 + 5x) 6ln + 6lnx = (2 * ln + 5x * ln) 6ln + 6lnx = (2ln + 5lnx) Solving 6ln + 6lnx = 2ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2ln' to each side of the equation. 6ln + -2ln + 6lnx = 2ln + -2ln + 5lnx Combine like terms: 6ln + -2ln = 4ln 4ln + 6lnx = 2ln + -2ln + 5lnx Combine like terms: 2ln + -2ln = 0 4ln + 6lnx = 0 + 5lnx 4ln + 6lnx = 5lnx Add '-5lnx' to each side of the equation. 4ln + 6lnx + -5lnx = 5lnx + -5lnx Combine like terms: 6lnx + -5lnx = 1lnx 4ln + 1lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 4ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(4 + 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 '(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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