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Simplifying 2ln(x + 2) = ln(x + 14) Reorder the terms: 2ln(2 + x) = ln(x + 14) (2 * 2ln + x * 2ln) = ln(x + 14) (4ln + 2lnx) = ln(x + 14) Reorder the terms: 4ln + 2lnx = ln(14 + x) 4ln + 2lnx = (14 * ln + x * ln) 4ln + 2lnx = (14ln + lnx) Solving 4ln + 2lnx = 14ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-14ln' to each side of the equation. 4ln + -14ln + 2lnx = 14ln + -14ln + lnx Combine like terms: 4ln + -14ln = -10ln -10ln + 2lnx = 14ln + -14ln + lnx Combine like terms: 14ln + -14ln = 0 -10ln + 2lnx = 0 + lnx -10ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -10ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -10ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -10ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-10 + x) = 0Subproblem 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 '(-10 + x)' equal to zero and attempt to solve: Simplifying -10 + x = 0 Solving -10 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x = 0 + 10 x = 0 + 10 Combine like terms: 0 + 10 = 10 x = 10 Add '-1x' to each side of the equation. x + -1x = 10 + -1x Combine like terms: x + -1x = 0 0 = 10 + -1x Simplifying 0 = 10 + -1x 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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