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