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Simplifying ln(48 + -20x) + -1ln(2) = 2ln(x) (48 * ln + -20x * ln) + -1ln(2) = 2ln(x) (48ln + -20lnx) + -1ln(2) = 2ln(x) Reorder the terms for easier multiplication: 48ln + -20lnx + -1 * 2ln = 2ln(x) Multiply -1 * 2 48ln + -20lnx + -2ln = 2ln(x) Reorder the terms: 48ln + -2ln + -20lnx = 2ln(x) Combine like terms: 48ln + -2ln = 46ln 46ln + -20lnx = 2ln(x) Multiply ln * x 46ln + -20lnx = 2lnx Solving 46ln + -20lnx = 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2lnx' to each side of the equation. 46ln + -20lnx + -2lnx = 2lnx + -2lnx Combine like terms: -20lnx + -2lnx = -22lnx 46ln + -22lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 46ln + -22lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(23 + -11x) = 0 Ignore the factor 2.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 '(23 + -11x)' equal to zero and attempt to solve: Simplifying 23 + -11x = 0 Solving 23 + -11x = 0 Move all terms containing l to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + -11x = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -11x = 0 + -23 -11x = 0 + -23 Combine like terms: 0 + -23 = -23 -11x = -23 Add '11x' to each side of the equation. -11x + 11x = -23 + 11x Combine like terms: -11x + 11x = 0 0 = -23 + 11x Simplifying 0 = -23 + 11x 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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