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Simplifying ln(4x + -9) + ln(3x) = 2lnx Reorder the terms: ln(-9 + 4x) + ln(3x) = 2lnx (-9 * ln + 4x * ln) + ln(3x) = 2lnx (-9ln + 4lnx) + ln(3x) = 2lnx Remove parenthesis around (3x) -9ln + 4lnx + ln * 3x = 2lnx Reorder the terms for easier multiplication: -9ln + 4lnx + 3ln * x = 2lnx Multiply ln * x -9ln + 4lnx + 3lnx = 2lnx Combine like terms: 4lnx + 3lnx = 7lnx -9ln + 7lnx = 2lnx Solving -9ln + 7lnx = 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2lnx' to each side of the equation. -9ln + 7lnx + -2lnx = 2lnx + -2lnx Combine like terms: 7lnx + -2lnx = 5lnx -9ln + 5lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -9ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-9 + 5x) = 0Subproblem 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 '(-9 + 5x)' equal to zero and attempt to solve: Simplifying -9 + 5x = 0 Solving -9 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 5x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 5x = 0 + 9 5x = 0 + 9 Combine like terms: 0 + 9 = 9 5x = 9 Add '-5x' to each side of the equation. 5x + -5x = 9 + -5x Combine like terms: 5x + -5x = 0 0 = 9 + -5x Simplifying 0 = 9 + -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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