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Simplifying ln(x + 35) + -1ln(x + -1) = ln(x + -5) Reorder the terms: ln(35 + x) + -1ln(x + -1) = ln(x + -5) (35 * ln + x * ln) + -1ln(x + -1) = ln(x + -5) (35ln + lnx) + -1ln(x + -1) = ln(x + -5) Reorder the terms: 35ln + lnx + -1ln(-1 + x) = ln(x + -5) 35ln + lnx + (-1 * -1ln + x * -1ln) = ln(x + -5) 35ln + lnx + (1ln + -1lnx) = ln(x + -5) Reorder the terms: 35ln + 1ln + lnx + -1lnx = ln(x + -5) Combine like terms: 35ln + 1ln = 36ln 36ln + lnx + -1lnx = ln(x + -5) Combine like terms: lnx + -1lnx = 0 36ln + 0 = ln(x + -5) 36ln = ln(x + -5) Reorder the terms: 36ln = ln(-5 + x) 36ln = (-5 * ln + x * ln) 36ln = (-5ln + lnx) Solving 36ln = -5ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '5ln' to each side of the equation. 36ln + 5ln = -5ln + 5ln + lnx Combine like terms: 36ln + 5ln = 41ln 41ln = -5ln + 5ln + lnx Combine like terms: -5ln + 5ln = 0 41ln = 0 + lnx 41ln = lnx Add '-1lnx' to each side of the equation. 41ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 41ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(41 + -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 '(41 + -1x)' equal to zero and attempt to solve: Simplifying 41 + -1x = 0 Solving 41 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-41' to each side of the equation. 41 + -41 + -1x = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -1x = 0 + -41 -1x = 0 + -41 Combine like terms: 0 + -41 = -41 -1x = -41 Add 'x' to each side of the equation. -1x + x = -41 + x Combine like terms: -1x + x = 0 0 = -41 + x Simplifying 0 = -41 + 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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