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Simplifying ln(2 + -1x) = ln(5x) (2 * ln + -1x * ln) = ln(5x) (2ln + -1lnx) = ln(5x) Remove parenthesis around (5x) 2ln + -1lnx = ln * 5x Reorder the terms for easier multiplication: 2ln + -1lnx = 5ln * x Multiply ln * x 2ln + -1lnx = 5lnx Solving 2ln + -1lnx = 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5lnx' to each side of the equation. 2ln + -1lnx + -5lnx = 5lnx + -5lnx Combine like terms: -1lnx + -5lnx = -6lnx 2ln + -6lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 2ln + -6lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(1 + -3x) = 0 Ignore the factor 2.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 '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Add '3x' to each side of the equation. -3x + 3x = -1 + 3x Combine like terms: -3x + 3x = 0 0 = -1 + 3x Simplifying 0 = -1 + 3x 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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