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Simplifying (1 + -1x) * ln(9) = (2x + 9) * ln(3) Reorder the terms for easier multiplication: 9ln(1 + -1x) = (2x + 9) * ln(3) (1 * 9ln + -1x * 9ln) = (2x + 9) * ln(3) (9ln + -9lnx) = (2x + 9) * ln(3) Reorder the terms: 9ln + -9lnx = (9 + 2x) * ln(3) Reorder the terms for easier multiplication: 9ln + -9lnx = 3ln(9 + 2x) 9ln + -9lnx = (9 * 3ln + 2x * 3ln) 9ln + -9lnx = (27ln + 6lnx) Solving 9ln + -9lnx = 27ln + 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-27ln' to each side of the equation. 9ln + -27ln + -9lnx = 27ln + -27ln + 6lnx Combine like terms: 9ln + -27ln = -18ln -18ln + -9lnx = 27ln + -27ln + 6lnx Combine like terms: 27ln + -27ln = 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 = -15lnx -18ln + -15lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 -18ln + -15lnx = 0 Factor out the Greatest Common Factor (GCF), '-3ln'. -3ln(6 + 5x) = 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 + 5x)' equal to zero and attempt to solve: Simplifying 6 + 5x = 0 Solving 6 + 5x = 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 + 5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5x = 0 + -6 5x = 0 + -6 Combine like terms: 0 + -6 = -6 5x = -6 Add '-5x' to each side of the equation. 5x + -5x = -6 + -5x Combine like terms: 5x + -5x = 0 0 = -6 + -5x Simplifying 0 = -6 + -5x 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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