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Simplifying ln(9750 + -1750x) = ln(10000 + -2000x) (9750 * ln + -1750x * ln) = ln(10000 + -2000x) (9750ln + -1750lnx) = ln(10000 + -2000x) 9750ln + -1750lnx = (10000 * ln + -2000x * ln) 9750ln + -1750lnx = (10000ln + -2000lnx) Solving 9750ln + -1750lnx = 10000ln + -2000lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10000ln' to each side of the equation. 9750ln + -10000ln + -1750lnx = 10000ln + -10000ln + -2000lnx Combine like terms: 9750ln + -10000ln = -250ln -250ln + -1750lnx = 10000ln + -10000ln + -2000lnx Combine like terms: 10000ln + -10000ln = 0 -250ln + -1750lnx = 0 + -2000lnx -250ln + -1750lnx = -2000lnx Add '2000lnx' to each side of the equation. -250ln + -1750lnx + 2000lnx = -2000lnx + 2000lnx Combine like terms: -1750lnx + 2000lnx = 250lnx -250ln + 250lnx = -2000lnx + 2000lnx Combine like terms: -2000lnx + 2000lnx = 0 -250ln + 250lnx = 0 Factor out the Greatest Common Factor (GCF), '250ln'. 250ln(-1 + x) = 0 Ignore the factor 250.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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