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