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Simplifying ln(7 + -2x) = ln(3x + -3) (7 * ln + -2x * ln) = ln(3x + -3) (7ln + -2lnx) = ln(3x + -3) Reorder the terms: 7ln + -2lnx = ln(-3 + 3x) 7ln + -2lnx = (-3 * ln + 3x * ln) 7ln + -2lnx = (-3ln + 3lnx) Solving 7ln + -2lnx = -3ln + 3lnx 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 + -2lnx = -3ln + 3ln + 3lnx Combine like terms: 7ln + 3ln = 10ln 10ln + -2lnx = -3ln + 3ln + 3lnx Combine like terms: -3ln + 3ln = 0 10ln + -2lnx = 0 + 3lnx 10ln + -2lnx = 3lnx Add '-3lnx' to each side of the equation. 10ln + -2lnx + -3lnx = 3lnx + -3lnx Combine like terms: -2lnx + -3lnx = -5lnx 10ln + -5lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 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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