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Simplifying ln(x + 9) = ln(4x + 36) + -1lnx Reorder the terms: ln(9 + x) = ln(4x + 36) + -1lnx (9 * ln + x * ln) = ln(4x + 36) + -1lnx (9ln + lnx) = ln(4x + 36) + -1lnx Reorder the terms: 9ln + lnx = ln(36 + 4x) + -1lnx 9ln + lnx = (36 * ln + 4x * ln) + -1lnx 9ln + lnx = (36ln + 4lnx) + -1lnx Combine like terms: 4lnx + -1lnx = 3lnx 9ln + lnx = 36ln + 3lnx Solving 9ln + lnx = 36ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-36ln' to each side of the equation. 9ln + -36ln + lnx = 36ln + -36ln + 3lnx Combine like terms: 9ln + -36ln = -27ln -27ln + lnx = 36ln + -36ln + 3lnx Combine like terms: 36ln + -36ln = 0 -27ln + lnx = 0 + 3lnx -27ln + lnx = 3lnx Add '-3lnx' to each side of the equation. -27ln + lnx + -3lnx = 3lnx + -3lnx Combine like terms: lnx + -3lnx = -2lnx -27ln + -2lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -27ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(27 + 2x) = 0 Ignore the factor -1.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 '(27 + 2x)' equal to zero and attempt to solve: Simplifying 27 + 2x = 0 Solving 27 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + 2x = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 2x = 0 + -27 2x = 0 + -27 Combine like terms: 0 + -27 = -27 2x = -27 Add '-2x' to each side of the equation. 2x + -2x = -27 + -2x Combine like terms: 2x + -2x = 0 0 = -27 + -2x Simplifying 0 = -27 + -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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