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Simplifying ln(6) = ln(x + 2) + -1ln(3) Reorder the terms for easier multiplication: 6ln = ln(x + 2) + -1ln(3) Reorder the terms: 6ln = ln(2 + x) + -1ln(3) 6ln = (2 * ln + x * ln) + -1ln(3) 6ln = (2ln + lnx) + -1ln(3) Reorder the terms for easier multiplication: 6ln = 2ln + lnx + -1 * 3ln Multiply -1 * 3 6ln = 2ln + lnx + -3ln Reorder the terms: 6ln = 2ln + -3ln + lnx Combine like terms: 2ln + -3ln = -1ln 6ln = -1ln + lnx Solving 6ln = -1ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'ln' to each side of the equation. 6ln + ln = -1ln + ln + lnx Combine like terms: 6ln + ln = 7ln 7ln = -1ln + ln + lnx Combine like terms: -1ln + ln = 0 7ln = 0 + lnx 7ln = lnx Add '-1lnx' to each side of the equation. 7ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 7ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(7 + -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 '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Add 'x' to each side of the equation. -1x + x = -7 + x Combine like terms: -1x + x = 0 0 = -7 + x Simplifying 0 = -7 + 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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