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Simplifying ln(56 + x) = log(-50 + -1x) (56 * ln + x * ln) = log(-50 + -1x) (56ln + lnx) = log(-50 + -1x) 56ln + lnx = (-50 * glo + -1x * glo) 56ln + lnx = (-50glo + -1glox) Solving 56ln + lnx = -50glo + -1glox Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '50glo' to each side of the equation. 56ln + 50glo + lnx = -50glo + 50glo + -1glox Reorder the terms: 50glo + 56ln + lnx = -50glo + 50glo + -1glox Combine like terms: -50glo + 50glo = 0 50glo + 56ln + lnx = 0 + -1glox 50glo + 56ln + lnx = -1glox Add 'glox' to each side of the equation. 50glo + 56ln + glox + lnx = -1glox + glox Reorder the terms: 50glo + glox + 56ln + lnx = -1glox + glox Combine like terms: -1glox + glox = 0 50glo + glox + 56ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'l'. l(50go + gox + 56n + nx) = 0Subproblem 1
Set the factor 'l' equal to zero and attempt to solve: Simplifying l = 0 Solving l = 0 Move all terms containing l to the left, all other terms to the right. Simplifying l = 0Subproblem 2
Set the factor '(50go + gox + 56n + nx)' equal to zero and attempt to solve: Simplifying 50go + gox + 56n + nx = 0 Solving 50go + gox + 56n + nx = 0 Move all terms containing l to the left, all other terms to the right. Add '-50go' to each side of the equation. 50go + gox + 56n + -50go + nx = 0 + -50go Reorder the terms: 50go + -50go + gox + 56n + nx = 0 + -50go Combine like terms: 50go + -50go = 0 0 + gox + 56n + nx = 0 + -50go gox + 56n + nx = 0 + -50go Remove the zero: gox + 56n + nx = -50go Add '-1gox' to each side of the equation. gox + 56n + -1gox + nx = -50go + -1gox Reorder the terms: gox + -1gox + 56n + nx = -50go + -1gox Combine like terms: gox + -1gox = 0 0 + 56n + nx = -50go + -1gox 56n + nx = -50go + -1gox Add '-56n' to each side of the equation. 56n + -56n + nx = -50go + -1gox + -56n Combine like terms: 56n + -56n = 0 0 + nx = -50go + -1gox + -56n nx = -50go + -1gox + -56n Add '-1nx' to each side of the equation. nx + -1nx = -50go + -1gox + -56n + -1nx Combine like terms: nx + -1nx = 0 0 = -50go + -1gox + -56n + -1nx Simplifying 0 = -50go + -1gox + -56n + -1nx The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
l = {0}
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