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Simplifying 100 = 10ln(x + 2) + 50 Reorder the terms: 100 = 10ln(2 + x) + 50 100 = (2 * 10ln + x * 10ln) + 50 100 = (20ln + 10lnx) + 50 Reorder the terms: 100 = 50 + 20ln + 10lnx Solving 100 = 50 + 20ln + 10lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-20ln' to each side of the equation. 100 + -20ln = 50 + 20ln + -20ln + 10lnx Combine like terms: 20ln + -20ln = 0 100 + -20ln = 50 + 0 + 10lnx 100 + -20ln = 50 + 10lnx Add '-10lnx' to each side of the equation. 100 + -20ln + -10lnx = 50 + 10lnx + -10lnx Combine like terms: 10lnx + -10lnx = 0 100 + -20ln + -10lnx = 50 + 0 100 + -20ln + -10lnx = 50 Add '-100' to each side of the equation. 100 + -20ln + -100 + -10lnx = 50 + -100 Reorder the terms: 100 + -100 + -20ln + -10lnx = 50 + -100 Combine like terms: 100 + -100 = 0 0 + -20ln + -10lnx = 50 + -100 -20ln + -10lnx = 50 + -100 Combine like terms: 50 + -100 = -50 -20ln + -10lnx = -50 Reorder the terms: 50 + -20ln + -10lnx = -50 + 50 Combine like terms: -50 + 50 = 0 50 + -20ln + -10lnx = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(5 + -2ln + -1lnx) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(5 + -2ln + -1lnx)' equal to zero and attempt to solve: Simplifying 5 + -2ln + -1lnx = 0 Solving 5 + -2ln + -1lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -2ln + -5 + -1lnx = 0 + -5 Reorder the terms: 5 + -5 + -2ln + -1lnx = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2ln + -1lnx = 0 + -5 -2ln + -1lnx = 0 + -5 Combine like terms: 0 + -5 = -5 -2ln + -1lnx = -5 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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