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Simplifying ln(2 + -1x) + ln(5 + -1x) = ln(37 + -1x) (2 * ln + -1x * ln) + ln(5 + -1x) = ln(37 + -1x) (2ln + -1lnx) + ln(5 + -1x) = ln(37 + -1x) 2ln + -1lnx + (5 * ln + -1x * ln) = ln(37 + -1x) 2ln + -1lnx + (5ln + -1lnx) = ln(37 + -1x) Reorder the terms: 2ln + 5ln + -1lnx + -1lnx = ln(37 + -1x) Combine like terms: 2ln + 5ln = 7ln 7ln + -1lnx + -1lnx = ln(37 + -1x) Combine like terms: -1lnx + -1lnx = -2lnx 7ln + -2lnx = ln(37 + -1x) 7ln + -2lnx = (37 * ln + -1x * ln) 7ln + -2lnx = (37ln + -1lnx) Solving 7ln + -2lnx = 37ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-37ln' to each side of the equation. 7ln + -37ln + -2lnx = 37ln + -37ln + -1lnx Combine like terms: 7ln + -37ln = -30ln -30ln + -2lnx = 37ln + -37ln + -1lnx Combine like terms: 37ln + -37ln = 0 -30ln + -2lnx = 0 + -1lnx -30ln + -2lnx = -1lnx Add 'lnx' to each side of the equation. -30ln + -2lnx + lnx = -1lnx + lnx Combine like terms: -2lnx + lnx = -1lnx -30ln + -1lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -30ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(30 + 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 '(30 + x)' equal to zero and attempt to solve: Simplifying 30 + x = 0 Solving 30 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 0 + -30 Combine like terms: 30 + -30 = 0 0 + x = 0 + -30 x = 0 + -30 Combine like terms: 0 + -30 = -30 x = -30 Add '-1x' to each side of the equation. x + -1x = -30 + -1x Combine like terms: x + -1x = 0 0 = -30 + -1x Simplifying 0 = -30 + -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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