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Simplifying ln(2x + 13) + ln(x + -6) + -2ln(x) = 0 Reorder the terms: ln(13 + 2x) + ln(x + -6) + -2ln(x) = 0 (13 * ln + 2x * ln) + ln(x + -6) + -2ln(x) = 0 (13ln + 2lnx) + ln(x + -6) + -2ln(x) = 0 Reorder the terms: 13ln + 2lnx + ln(-6 + x) + -2ln(x) = 0 13ln + 2lnx + (-6 * ln + x * ln) + -2ln(x) = 0 13ln + 2lnx + (-6ln + lnx) + -2ln(x) = 0 Multiply ln * x 13ln + 2lnx + -6ln + lnx + -2lnx = 0 Reorder the terms: 13ln + -6ln + 2lnx + lnx + -2lnx = 0 Combine like terms: 13ln + -6ln = 7ln 7ln + 2lnx + lnx + -2lnx = 0 Combine like terms: 2lnx + lnx = 3lnx 7ln + 3lnx + -2lnx = 0 Combine like terms: 3lnx + -2lnx = 1lnx 7ln + 1lnx = 0 Solving 7ln + 1lnx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'ln'. ln(7 + x) = 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 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Add '-1x' to each side of the equation. x + -1x = -7 + -1x Combine like terms: x + -1x = 0 0 = -7 + -1x Simplifying 0 = -7 + -1x 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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