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Simplifying ln(10 + -1x) = 2ln(x + 2) (10 * ln + -1x * ln) = 2ln(x + 2) (10ln + -1lnx) = 2ln(x + 2) Reorder the terms: 10ln + -1lnx = 2ln(2 + x) 10ln + -1lnx = (2 * 2ln + x * 2ln) 10ln + -1lnx = (4ln + 2lnx) Solving 10ln + -1lnx = 4ln + 2lnx 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. 10ln + -4ln + -1lnx = 4ln + -4ln + 2lnx Combine like terms: 10ln + -4ln = 6ln 6ln + -1lnx = 4ln + -4ln + 2lnx Combine like terms: 4ln + -4ln = 0 6ln + -1lnx = 0 + 2lnx 6ln + -1lnx = 2lnx Add '-2lnx' to each side of the equation. 6ln + -1lnx + -2lnx = 2lnx + -2lnx Combine like terms: -1lnx + -2lnx = -3lnx 6ln + -3lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 6ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(2 + -1x) = 0 Ignore the factor 3.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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