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Simplifying ln(x + -2) + -1ln(x + 5) = lm(x + -1) + -1ln(x + 11) Reorder the terms: ln(-2 + x) + -1ln(x + 5) = lm(x + -1) + -1ln(x + 11) (-2 * ln + x * ln) + -1ln(x + 5) = lm(x + -1) + -1ln(x + 11) (-2ln + lnx) + -1ln(x + 5) = lm(x + -1) + -1ln(x + 11) Reorder the terms: -2ln + lnx + -1ln(5 + x) = lm(x + -1) + -1ln(x + 11) -2ln + lnx + (5 * -1ln + x * -1ln) = lm(x + -1) + -1ln(x + 11) -2ln + lnx + (-5ln + -1lnx) = lm(x + -1) + -1ln(x + 11) Reorder the terms: -2ln + -5ln + lnx + -1lnx = lm(x + -1) + -1ln(x + 11) Combine like terms: -2ln + -5ln = -7ln -7ln + lnx + -1lnx = lm(x + -1) + -1ln(x + 11) Combine like terms: lnx + -1lnx = 0 -7ln + 0 = lm(x + -1) + -1ln(x + 11) -7ln = lm(x + -1) + -1ln(x + 11) Reorder the terms: -7ln = lm(-1 + x) + -1ln(x + 11) -7ln = (-1 * lm + x * lm) + -1ln(x + 11) -7ln = (-1lm + lmx) + -1ln(x + 11) Reorder the terms: -7ln = -1lm + lmx + -1ln(11 + x) -7ln = -1lm + lmx + (11 * -1ln + x * -1ln) -7ln = -1lm + lmx + (-11ln + -1lnx) Solving -7ln = -1lm + lmx + -11ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'lm' to each side of the equation. lm + -7ln = -1lm + lmx + -11ln + lm + -1lnx Reorder the terms: lm + -7ln = -1lm + lm + lmx + -11ln + -1lnx Combine like terms: -1lm + lm = 0 lm + -7ln = 0 + lmx + -11ln + -1lnx lm + -7ln = lmx + -11ln + -1lnx Add '-1lmx' to each side of the equation. lm + -1lmx + -7ln = lmx + -11ln + -1lmx + -1lnx Reorder the terms: lm + -1lmx + -7ln = lmx + -1lmx + -11ln + -1lnx Combine like terms: lmx + -1lmx = 0 lm + -1lmx + -7ln = 0 + -11ln + -1lnx lm + -1lmx + -7ln = -11ln + -1lnx Add '11ln' to each side of the equation. lm + -1lmx + -7ln + 11ln = -11ln + 11ln + -1lnx Combine like terms: -7ln + 11ln = 4ln lm + -1lmx + 4ln = -11ln + 11ln + -1lnx Combine like terms: -11ln + 11ln = 0 lm + -1lmx + 4ln = 0 + -1lnx lm + -1lmx + 4ln = -1lnx Add 'lnx' to each side of the equation. lm + -1lmx + 4ln + lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 lm + -1lmx + 4ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'l'. l(m + -1mx + 4n + 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 '(m + -1mx + 4n + nx)' equal to zero and attempt to solve: Simplifying m + -1mx + 4n + nx = 0 Solving m + -1mx + 4n + nx = 0 Move all terms containing l to the left, all other terms to the right. Add '-1m' to each side of the equation. m + -1mx + 4n + -1m + nx = 0 + -1m Reorder the terms: m + -1m + -1mx + 4n + nx = 0 + -1m Combine like terms: m + -1m = 0 0 + -1mx + 4n + nx = 0 + -1m -1mx + 4n + nx = 0 + -1m Remove the zero: -1mx + 4n + nx = -1m Add 'mx' to each side of the equation. -1mx + 4n + mx + nx = -1m + mx Reorder the terms: -1mx + mx + 4n + nx = -1m + mx Combine like terms: -1mx + mx = 0 0 + 4n + nx = -1m + mx 4n + nx = -1m + mx Add '-4n' to each side of the equation. 4n + -4n + nx = -1m + mx + -4n Combine like terms: 4n + -4n = 0 0 + nx = -1m + mx + -4n nx = -1m + mx + -4n Add '-1nx' to each side of the equation. nx + -1nx = -1m + mx + -4n + -1nx Combine like terms: nx + -1nx = 0 0 = -1m + mx + -4n + -1nx Simplifying 0 = -1m + mx + -4n + -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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