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Simplifying (x + 6) * ln * 15 = (x + -6) * ln * 100 Reorder the terms: (6 + x) * ln * 15 = (x + -6) * ln * 100 Reorder the terms for easier multiplication: 15ln(6 + x) = (x + -6) * ln * 100 (6 * 15ln + x * 15ln) = (x + -6) * ln * 100 (90ln + 15lnx) = (x + -6) * ln * 100 Reorder the terms: 90ln + 15lnx = (-6 + x) * ln * 100 Reorder the terms for easier multiplication: 90ln + 15lnx = 100ln(-6 + x) 90ln + 15lnx = (-6 * 100ln + x * 100ln) 90ln + 15lnx = (-600ln + 100lnx) Solving 90ln + 15lnx = -600ln + 100lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '600ln' to each side of the equation. 90ln + 600ln + 15lnx = -600ln + 600ln + 100lnx Combine like terms: 90ln + 600ln = 690ln 690ln + 15lnx = -600ln + 600ln + 100lnx Combine like terms: -600ln + 600ln = 0 690ln + 15lnx = 0 + 100lnx 690ln + 15lnx = 100lnx Add '-100lnx' to each side of the equation. 690ln + 15lnx + -100lnx = 100lnx + -100lnx Combine like terms: 15lnx + -100lnx = -85lnx 690ln + -85lnx = 100lnx + -100lnx Combine like terms: 100lnx + -100lnx = 0 690ln + -85lnx = 0 Factor out the Greatest Common Factor (GCF), '5ln'. 5ln(138 + -17x) = 0 Ignore the factor 5.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 '(138 + -17x)' equal to zero and attempt to solve: Simplifying 138 + -17x = 0 Solving 138 + -17x = 0 Move all terms containing l to the left, all other terms to the right. Add '-138' to each side of the equation. 138 + -138 + -17x = 0 + -138 Combine like terms: 138 + -138 = 0 0 + -17x = 0 + -138 -17x = 0 + -138 Combine like terms: 0 + -138 = -138 -17x = -138 Add '17x' to each side of the equation. -17x + 17x = -138 + 17x Combine like terms: -17x + 17x = 0 0 = -138 + 17x Simplifying 0 = -138 + 17x 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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