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Simplifying ln(x) + ln(x + -6) = ln(8x + -24) Multiply ln * x lnx + ln(x + -6) = ln(8x + -24) Reorder the terms: lnx + ln(-6 + x) = ln(8x + -24) lnx + (-6 * ln + x * ln) = ln(8x + -24) lnx + (-6ln + lnx) = ln(8x + -24) Reorder the terms: -6ln + lnx + lnx = ln(8x + -24) Combine like terms: lnx + lnx = 2lnx -6ln + 2lnx = ln(8x + -24) Reorder the terms: -6ln + 2lnx = ln(-24 + 8x) -6ln + 2lnx = (-24 * ln + 8x * ln) -6ln + 2lnx = (-24ln + 8lnx) Solving -6ln + 2lnx = -24ln + 8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '24ln' to each side of the equation. -6ln + 24ln + 2lnx = -24ln + 24ln + 8lnx Combine like terms: -6ln + 24ln = 18ln 18ln + 2lnx = -24ln + 24ln + 8lnx Combine like terms: -24ln + 24ln = 0 18ln + 2lnx = 0 + 8lnx 18ln + 2lnx = 8lnx Add '-8lnx' to each side of the equation. 18ln + 2lnx + -8lnx = 8lnx + -8lnx Combine like terms: 2lnx + -8lnx = -6lnx 18ln + -6lnx = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 18ln + -6lnx = 0 Factor out the Greatest Common Factor (GCF), '6ln'. 6ln(3 + -1x) = 0 Ignore the factor 6.Subproblem 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + 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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