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Simplifying ln(x) + ln(x + -6) = ln(x + 8) Multiply ln * x lnx + ln(x + -6) = ln(x + 8) Reorder the terms: lnx + ln(-6 + x) = ln(x + 8) lnx + (-6 * ln + x * ln) = ln(x + 8) lnx + (-6ln + lnx) = ln(x + 8) Reorder the terms: -6ln + lnx + lnx = ln(x + 8) Combine like terms: lnx + lnx = 2lnx -6ln + 2lnx = ln(x + 8) Reorder the terms: -6ln + 2lnx = ln(8 + x) -6ln + 2lnx = (8 * ln + x * ln) -6ln + 2lnx = (8ln + lnx) Solving -6ln + 2lnx = 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. -6ln + -8ln + 2lnx = 8ln + -8ln + lnx Combine like terms: -6ln + -8ln = -14ln -14ln + 2lnx = 8ln + -8ln + lnx Combine like terms: 8ln + -8ln = 0 -14ln + 2lnx = 0 + lnx -14ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -14ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -14ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -14ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-14 + 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 '(-14 + x)' equal to zero and attempt to solve: Simplifying -14 + x = 0 Solving -14 + x = 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 + x = 0 + 14 Combine like terms: -14 + 14 = 0 0 + x = 0 + 14 x = 0 + 14 Combine like terms: 0 + 14 = 14 x = 14 Add '-1x' to each side of the equation. x + -1x = 14 + -1x Combine like terms: x + -1x = 0 0 = 14 + -1x Simplifying 0 = 14 + -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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