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Simplifying lny = ln(1 + -1exp(-1x)) Remove parenthesis around (-1x) lny = ln(1 + -1epx * -1x) Reorder the terms for easier multiplication: lny = ln(1 + -1 * -1epx * x) Multiply -1 * -1 lny = ln(1 + 1epx * x) Multiply epx * x lny = ln(1 + 1epx2) lny = (1 * ln + 1epx2 * ln) Reorder the terms: lny = (1elnpx2 + 1ln) lny = (1elnpx2 + 1ln) Solving lny = 1elnpx2 + 1ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1elnpx2' to each side of the equation. -1elnpx2 + lny = 1elnpx2 + -1elnpx2 + 1ln Combine like terms: 1elnpx2 + -1elnpx2 = 0 -1elnpx2 + lny = 0 + 1ln -1elnpx2 + lny = 1ln Add '-1ln' to each side of the equation. -1elnpx2 + -1ln + lny = 1ln + -1ln Combine like terms: 1ln + -1ln = 0 -1elnpx2 + -1ln + lny = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-1epx2 + -1 + y) = 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 '(-1epx2 + -1 + y)' equal to zero and attempt to solve: Simplifying -1epx2 + -1 + y = 0 Reorder the terms: -1 + -1epx2 + y = 0 Solving -1 + -1epx2 + y = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -1epx2 + 1 + y = 0 + 1 Reorder the terms: -1 + 1 + -1epx2 + y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1epx2 + y = 0 + 1 -1epx2 + y = 0 + 1 Combine like terms: 0 + 1 = 1 -1epx2 + y = 1 Add 'epx2' to each side of the equation. -1epx2 + epx2 + y = 1 + epx2 Combine like terms: -1epx2 + epx2 = 0 0 + y = 1 + epx2 y = 1 + epx2 Add '-1y' to each side of the equation. y + -1y = 1 + epx2 + -1y Combine like terms: y + -1y = 0 0 = 1 + epx2 + -1y Simplifying 0 = 1 + epx2 + -1y 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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