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Simplifying ln(x) = ln(x + 9) + ln(x + -8) Multiply ln * x lnx = ln(x + 9) + ln(x + -8) Reorder the terms: lnx = ln(9 + x) + ln(x + -8) lnx = (9 * ln + x * ln) + ln(x + -8) lnx = (9ln + lnx) + ln(x + -8) Reorder the terms: lnx = 9ln + lnx + ln(-8 + x) lnx = 9ln + lnx + (-8 * ln + x * ln) lnx = 9ln + lnx + (-8ln + lnx) Reorder the terms: lnx = 9ln + -8ln + lnx + lnx Combine like terms: 9ln + -8ln = 1ln lnx = 1ln + lnx + lnx Combine like terms: lnx + lnx = 2lnx lnx = 1ln + 2lnx Solving lnx = 1ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. -1ln + lnx = 1ln + -1ln + 2lnx Combine like terms: 1ln + -1ln = 0 -1ln + lnx = 0 + 2lnx -1ln + lnx = 2lnx Add '-2lnx' to each side of the equation. -1ln + lnx + -2lnx = 2lnx + -2lnx Combine like terms: lnx + -2lnx = -1lnx -1ln + -1lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -1ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(1 + x) = 0 Ignore the factor -1.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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -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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