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Simplifying ln(x) + ln(2 + -1x) = ln(5x) + -1ln(x + 4) Multiply ln * x lnx + ln(2 + -1x) = ln(5x) + -1ln(x + 4) lnx + (2 * ln + -1x * ln) = ln(5x) + -1ln(x + 4) lnx + (2ln + -1lnx) = ln(5x) + -1ln(x + 4) Reorder the terms: 2ln + lnx + -1lnx = ln(5x) + -1ln(x + 4) Combine like terms: lnx + -1lnx = 0 2ln + 0 = ln(5x) + -1ln(x + 4) 2ln = ln(5x) + -1ln(x + 4) Remove parenthesis around (5x) 2ln = ln * 5x + -1ln(x + 4) Reorder the terms for easier multiplication: 2ln = 5ln * x + -1ln(x + 4) Multiply ln * x 2ln = 5lnx + -1ln(x + 4) Reorder the terms: 2ln = 5lnx + -1ln(4 + x) 2ln = 5lnx + (4 * -1ln + x * -1ln) 2ln = 5lnx + (-4ln + -1lnx) Reorder the terms: 2ln = -4ln + 5lnx + -1lnx Combine like terms: 5lnx + -1lnx = 4lnx 2ln = -4ln + 4lnx Solving 2ln = -4ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '4ln' to each side of the equation. 2ln + 4ln = -4ln + 4ln + 4lnx Combine like terms: 2ln + 4ln = 6ln 6ln = -4ln + 4ln + 4lnx Combine like terms: -4ln + 4ln = 0 6ln = 0 + 4lnx 6ln = 4lnx Add '-4lnx' to each side of the equation. 6ln + -4lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 6ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(3 + -2x) = 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 '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Add '2x' to each side of the equation. -2x + 2x = -3 + 2x Combine like terms: -2x + 2x = 0 0 = -3 + 2x Simplifying 0 = -3 + 2x 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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