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