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Simplifying 2lnx + -1ln(3x + -7) = ln(5x) + -1ln(x + 3) Reorder the terms: 2lnx + -1ln(-7 + 3x) = ln(5x) + -1ln(x + 3) 2lnx + (-7 * -1ln + 3x * -1ln) = ln(5x) + -1ln(x + 3) 2lnx + (7ln + -3lnx) = ln(5x) + -1ln(x + 3) Reorder the terms: 7ln + 2lnx + -3lnx = ln(5x) + -1ln(x + 3) Combine like terms: 2lnx + -3lnx = -1lnx 7ln + -1lnx = ln(5x) + -1ln(x + 3) Remove parenthesis around (5x) 7ln + -1lnx = ln * 5x + -1ln(x + 3) Reorder the terms for easier multiplication: 7ln + -1lnx = 5ln * x + -1ln(x + 3) Multiply ln * x 7ln + -1lnx = 5lnx + -1ln(x + 3) Reorder the terms: 7ln + -1lnx = 5lnx + -1ln(3 + x) 7ln + -1lnx = 5lnx + (3 * -1ln + x * -1ln) 7ln + -1lnx = 5lnx + (-3ln + -1lnx) Reorder the terms: 7ln + -1lnx = -3ln + 5lnx + -1lnx Combine like terms: 5lnx + -1lnx = 4lnx 7ln + -1lnx = -3ln + 4lnx Solving 7ln + -1lnx = -3ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '3ln' to each side of the equation. 7ln + 3ln + -1lnx = -3ln + 3ln + 4lnx Combine like terms: 7ln + 3ln = 10ln 10ln + -1lnx = -3ln + 3ln + 4lnx Combine like terms: -3ln + 3ln = 0 10ln + -1lnx = 0 + 4lnx 10ln + -1lnx = 4lnx Add '-4lnx' to each side of the equation. 10ln + -1lnx + -4lnx = 4lnx + -4lnx Combine like terms: -1lnx + -4lnx = -5lnx 10ln + -5lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 10ln + -5lnx = 0 Factor out the Greatest Common Factor (GCF), '5ln'. 5ln(2 + -1x) = 0 Ignore the factor 5.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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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