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Simplifying lnx + ln(x + -2) = ln(x + 24) Reorder the terms: lnx + ln(-2 + x) = ln(x + 24) lnx + (-2 * ln + x * ln) = ln(x + 24) lnx + (-2ln + lnx) = ln(x + 24) Reorder the terms: -2ln + lnx + lnx = ln(x + 24) Combine like terms: lnx + lnx = 2lnx -2ln + 2lnx = ln(x + 24) Reorder the terms: -2ln + 2lnx = ln(24 + x) -2ln + 2lnx = (24 * ln + x * ln) -2ln + 2lnx = (24ln + lnx) Solving -2ln + 2lnx = 24ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-24ln' to each side of the equation. -2ln + -24ln + 2lnx = 24ln + -24ln + lnx Combine like terms: -2ln + -24ln = -26ln -26ln + 2lnx = 24ln + -24ln + lnx Combine like terms: 24ln + -24ln = 0 -26ln + 2lnx = 0 + lnx -26ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -26ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -26ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -26ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-26 + x) = 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 '(-26 + x)' equal to zero and attempt to solve: Simplifying -26 + x = 0 Solving -26 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = 0 + 26 Combine like terms: -26 + 26 = 0 0 + x = 0 + 26 x = 0 + 26 Combine like terms: 0 + 26 = 26 x = 26 Add '-1x' to each side of the equation. x + -1x = 26 + -1x Combine like terms: x + -1x = 0 0 = 26 + -1x Simplifying 0 = 26 + -1x 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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