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