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