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Simplifying ln(x + -15) + ln(x + 2) = ln(-10x + -2) Reorder the terms: ln(-15 + x) + ln(x + 2) = ln(-10x + -2) (-15 * ln + x * ln) + ln(x + 2) = ln(-10x + -2) (-15ln + lnx) + ln(x + 2) = ln(-10x + -2) Reorder the terms: -15ln + lnx + ln(2 + x) = ln(-10x + -2) -15ln + lnx + (2 * ln + x * ln) = ln(-10x + -2) -15ln + lnx + (2ln + lnx) = ln(-10x + -2) Reorder the terms: -15ln + 2ln + lnx + lnx = ln(-10x + -2) Combine like terms: -15ln + 2ln = -13ln -13ln + lnx + lnx = ln(-10x + -2) Combine like terms: lnx + lnx = 2lnx -13ln + 2lnx = ln(-10x + -2) Reorder the terms: -13ln + 2lnx = ln(-2 + -10x) -13ln + 2lnx = (-2 * ln + -10x * ln) -13ln + 2lnx = (-2ln + -10lnx) Solving -13ln + 2lnx = -2ln + -10lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2ln' to each side of the equation. -13ln + 2ln + 2lnx = -2ln + 2ln + -10lnx Combine like terms: -13ln + 2ln = -11ln -11ln + 2lnx = -2ln + 2ln + -10lnx Combine like terms: -2ln + 2ln = 0 -11ln + 2lnx = 0 + -10lnx -11ln + 2lnx = -10lnx Add '10lnx' to each side of the equation. -11ln + 2lnx + 10lnx = -10lnx + 10lnx Combine like terms: 2lnx + 10lnx = 12lnx -11ln + 12lnx = -10lnx + 10lnx Combine like terms: -10lnx + 10lnx = 0 -11ln + 12lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-11 + 12x) = 0Subproblem 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 '(-11 + 12x)' equal to zero and attempt to solve: Simplifying -11 + 12x = 0 Solving -11 + 12x = 0 Move all terms containing l to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + 12x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 12x = 0 + 11 12x = 0 + 11 Combine like terms: 0 + 11 = 11 12x = 11 Add '-12x' to each side of the equation. 12x + -12x = 11 + -12x Combine like terms: 12x + -12x = 0 0 = 11 + -12x Simplifying 0 = 11 + -12x 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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