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Simplifying ln(4x + 6) + -1ln(x + 5) = lnx Reorder the terms: ln(6 + 4x) + -1ln(x + 5) = lnx (6 * ln + 4x * ln) + -1ln(x + 5) = lnx (6ln + 4lnx) + -1ln(x + 5) = lnx Reorder the terms: 6ln + 4lnx + -1ln(5 + x) = lnx 6ln + 4lnx + (5 * -1ln + x * -1ln) = lnx 6ln + 4lnx + (-5ln + -1lnx) = lnx Reorder the terms: 6ln + -5ln + 4lnx + -1lnx = lnx Combine like terms: 6ln + -5ln = 1ln 1ln + 4lnx + -1lnx = lnx Combine like terms: 4lnx + -1lnx = 3lnx 1ln + 3lnx = lnx Solving 1ln + 3lnx = lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnx' to each side of the equation. 1ln + 3lnx + -1lnx = lnx + -1lnx Combine like terms: 3lnx + -1lnx = 2lnx 1ln + 2lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 1ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + 2x) = 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 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -2x 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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