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Simplifying ln(13) = ln(x + 6) + -1ln(7) Reorder the terms for easier multiplication: 13ln = ln(x + 6) + -1ln(7) Reorder the terms: 13ln = ln(6 + x) + -1ln(7) 13ln = (6 * ln + x * ln) + -1ln(7) 13ln = (6ln + lnx) + -1ln(7) Reorder the terms for easier multiplication: 13ln = 6ln + lnx + -1 * 7ln Multiply -1 * 7 13ln = 6ln + lnx + -7ln Reorder the terms: 13ln = 6ln + -7ln + lnx Combine like terms: 6ln + -7ln = -1ln 13ln = -1ln + lnx Solving 13ln = -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. 13ln + ln = -1ln + ln + lnx Combine like terms: 13ln + ln = 14ln 14ln = -1ln + ln + lnx Combine like terms: -1ln + ln = 0 14ln = 0 + lnx 14ln = lnx Add '-1lnx' to each side of the equation. 14ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 14ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(14 + -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 '(14 + -1x)' equal to zero and attempt to solve: Simplifying 14 + -1x = 0 Solving 14 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1x = 0 + -14 -1x = 0 + -14 Combine like terms: 0 + -14 = -14 -1x = -14 Add 'x' to each side of the equation. -1x + x = -14 + x Combine like terms: -1x + x = 0 0 = -14 + x Simplifying 0 = -14 + 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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