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Simplifying ln(x + -1) + ln(x + -6) = ln(14) Reorder the terms: ln(-1 + x) + ln(x + -6) = ln(14) (-1 * ln + x * ln) + ln(x + -6) = ln(14) (-1ln + lnx) + ln(x + -6) = ln(14) Reorder the terms: -1ln + lnx + ln(-6 + x) = ln(14) -1ln + lnx + (-6 * ln + x * ln) = ln(14) -1ln + lnx + (-6ln + lnx) = ln(14) Reorder the terms: -1ln + -6ln + lnx + lnx = ln(14) Combine like terms: -1ln + -6ln = -7ln -7ln + lnx + lnx = ln(14) Combine like terms: lnx + lnx = 2lnx -7ln + 2lnx = ln(14) Reorder the terms for easier multiplication: -7ln + 2lnx = 14ln Solving -7ln + 2lnx = 14ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-14ln' to each side of the equation. -7ln + -14ln + 2lnx = 14ln + -14ln Combine like terms: -7ln + -14ln = -21ln -21ln + 2lnx = 14ln + -14ln Combine like terms: 14ln + -14ln = 0 -21ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-21 + 2x) = 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 '(-21 + 2x)' equal to zero and attempt to solve: Simplifying -21 + 2x = 0 Solving -21 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + 2x = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 2x = 0 + 21 2x = 0 + 21 Combine like terms: 0 + 21 = 21 2x = 21 Add '-2x' to each side of the equation. 2x + -2x = 21 + -2x Combine like terms: 2x + -2x = 0 0 = 21 + -2x Simplifying 0 = 21 + -2x 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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