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Simplifying ln(20) = ln(x + 6) + ln(2) Reorder the terms for easier multiplication: 20ln = ln(x + 6) + ln(2) Reorder the terms: 20ln = ln(6 + x) + ln(2) 20ln = (6 * ln + x * ln) + ln(2) 20ln = (6ln + lnx) + ln(2) Reorder the terms for easier multiplication: 20ln = 6ln + lnx + 2ln Reorder the terms: 20ln = 6ln + 2ln + lnx Combine like terms: 6ln + 2ln = 8ln 20ln = 8ln + lnx Solving 20ln = 8ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. 20ln + -8ln = 8ln + -8ln + lnx Combine like terms: 20ln + -8ln = 12ln 12ln = 8ln + -8ln + lnx Combine like terms: 8ln + -8ln = 0 12ln = 0 + lnx 12ln = lnx Add '-1lnx' to each side of the equation. 12ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 12ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(12 + -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 '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Add 'x' to each side of the equation. -1x + x = -12 + x Combine like terms: -1x + x = 0 0 = -12 + x Simplifying 0 = -12 + 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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