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Simplifying (x + 8) * ln * 25 = (x + -8) * ln * 125 Reorder the terms: (8 + x) * ln * 25 = (x + -8) * ln * 125 Reorder the terms for easier multiplication: 25ln(8 + x) = (x + -8) * ln * 125 (8 * 25ln + x * 25ln) = (x + -8) * ln * 125 (200ln + 25lnx) = (x + -8) * ln * 125 Reorder the terms: 200ln + 25lnx = (-8 + x) * ln * 125 Reorder the terms for easier multiplication: 200ln + 25lnx = 125ln(-8 + x) 200ln + 25lnx = (-8 * 125ln + x * 125ln) 200ln + 25lnx = (-1000ln + 125lnx) Solving 200ln + 25lnx = -1000ln + 125lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '1000ln' to each side of the equation. 200ln + 1000ln + 25lnx = -1000ln + 1000ln + 125lnx Combine like terms: 200ln + 1000ln = 1200ln 1200ln + 25lnx = -1000ln + 1000ln + 125lnx Combine like terms: -1000ln + 1000ln = 0 1200ln + 25lnx = 0 + 125lnx 1200ln + 25lnx = 125lnx Add '-125lnx' to each side of the equation. 1200ln + 25lnx + -125lnx = 125lnx + -125lnx Combine like terms: 25lnx + -125lnx = -100lnx 1200ln + -100lnx = 125lnx + -125lnx Combine like terms: 125lnx + -125lnx = 0 1200ln + -100lnx = 0 Factor out the Greatest Common Factor (GCF), '100ln'. 100ln(12 + -1x) = 0 Ignore the factor 100.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 '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Add 'x' to each side of the equation. -1x + x = -12 + x Combine like terms: -1x + x = 0 0 = -12 + x Simplifying 0 = -12 + x 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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