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