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Simplifying 2ln(x) + -1ln(4x + -5) = ln(2x) Multiply ln * x 2lnx + -1ln(4x + -5) = ln(2x) Reorder the terms: 2lnx + -1ln(-5 + 4x) = ln(2x) 2lnx + (-5 * -1ln + 4x * -1ln) = ln(2x) 2lnx + (5ln + -4lnx) = ln(2x) Reorder the terms: 5ln + 2lnx + -4lnx = ln(2x) Combine like terms: 2lnx + -4lnx = -2lnx 5ln + -2lnx = ln(2x) Remove parenthesis around (2x) 5ln + -2lnx = ln * 2x Reorder the terms for easier multiplication: 5ln + -2lnx = 2ln * x Multiply ln * x 5ln + -2lnx = 2lnx Solving 5ln + -2lnx = 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. 5ln + -2lnx + -2lnx = 2lnx + -2lnx Combine like terms: -2lnx + -2lnx = -4lnx 5ln + -4lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 5ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(5 + -4x) = 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 '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Add '4x' to each side of the equation. -4x + 4x = -5 + 4x Combine like terms: -4x + 4x = 0 0 = -5 + 4x Simplifying 0 = -5 + 4x 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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