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Simplifying ln(20) = ln(x + 1) + ln(2) Reorder the terms for easier multiplication: 20ln = ln(x + 1) + ln(2) Reorder the terms: 20ln = ln(1 + x) + ln(2) 20ln = (1 * ln + x * ln) + ln(2) 20ln = (1ln + lnx) + ln(2) Reorder the terms for easier multiplication: 20ln = 1ln + lnx + 2ln Reorder the terms: 20ln = 1ln + 2ln + lnx Combine like terms: 1ln + 2ln = 3ln 20ln = 3ln + lnx Solving 20ln = 3ln + lnx 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. 20ln + -3ln = 3ln + -3ln + lnx Combine like terms: 20ln + -3ln = 17ln 17ln = 3ln + -3ln + lnx Combine like terms: 3ln + -3ln = 0 17ln = 0 + lnx 17ln = lnx Add '-1lnx' to each side of the equation. 17ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 17ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(17 + -1x) = 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 '(17 + -1x)' equal to zero and attempt to solve: Simplifying 17 + -1x = 0 Solving 17 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -1x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -1x = 0 + -17 -1x = 0 + -17 Combine like terms: 0 + -17 = -17 -1x = -17 Add 'x' to each side of the equation. -1x + x = -17 + x Combine like terms: -1x + x = 0 0 = -17 + x Simplifying 0 = -17 + 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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