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Simplifying ln(x + 1) = ln(9x + -5) Reorder the terms: ln(1 + x) = ln(9x + -5) (1 * ln + x * ln) = ln(9x + -5) (1ln + lnx) = ln(9x + -5) Reorder the terms: 1ln + lnx = ln(-5 + 9x) 1ln + lnx = (-5 * ln + 9x * ln) 1ln + lnx = (-5ln + 9lnx) Solving 1ln + lnx = -5ln + 9lnx 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. 1ln + 5ln + lnx = -5ln + 5ln + 9lnx Combine like terms: 1ln + 5ln = 6ln 6ln + lnx = -5ln + 5ln + 9lnx Combine like terms: -5ln + 5ln = 0 6ln + lnx = 0 + 9lnx 6ln + lnx = 9lnx Add '-9lnx' to each side of the equation. 6ln + lnx + -9lnx = 9lnx + -9lnx Combine like terms: lnx + -9lnx = -8lnx 6ln + -8lnx = 9lnx + -9lnx Combine like terms: 9lnx + -9lnx = 0 6ln + -8lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(3 + -4x) = 0 Ignore the factor 2.Subproblem 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 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Add '4x' to each side of the equation. -4x + 4x = -3 + 4x Combine like terms: -4x + 4x = 0 0 = -3 + 4x Simplifying 0 = -3 + 4x 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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