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Simplifying ln(9x + 13) = ln(6x + -5) Reorder the terms: ln(13 + 9x) = ln(6x + -5) (13 * ln + 9x * ln) = ln(6x + -5) (13ln + 9lnx) = ln(6x + -5) Reorder the terms: 13ln + 9lnx = ln(-5 + 6x) 13ln + 9lnx = (-5 * ln + 6x * ln) 13ln + 9lnx = (-5ln + 6lnx) Solving 13ln + 9lnx = -5ln + 6lnx 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. 13ln + 5ln + 9lnx = -5ln + 5ln + 6lnx Combine like terms: 13ln + 5ln = 18ln 18ln + 9lnx = -5ln + 5ln + 6lnx Combine like terms: -5ln + 5ln = 0 18ln + 9lnx = 0 + 6lnx 18ln + 9lnx = 6lnx Add '-6lnx' to each side of the equation. 18ln + 9lnx + -6lnx = 6lnx + -6lnx Combine like terms: 9lnx + -6lnx = 3lnx 18ln + 3lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 18ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(6 + 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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -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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