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