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Simplifying lnx(lnx + -10) = 24 Reorder the terms: lnx(-10 + lnx) = 24 (-10 * lnx + lnx * lnx) = 24 (-10lnx + l2n2x2) = 24 Solving -10lnx + l2n2x2 = 24 Solving for variable 'l'. Reorder the terms: -24 + -10lnx + l2n2x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -10lnx + l2n2x2 = 0 Factor a trinomial. (-2 + -1lnx)(12 + -1lnx) = 0Subproblem 1
Set the factor '(-2 + -1lnx)' equal to zero and attempt to solve: Simplifying -2 + -1lnx = 0 Solving -2 + -1lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1lnx = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1lnx = 0 + 2 -1lnx = 0 + 2 Combine like terms: 0 + 2 = 2 -1lnx = 2 Divide each side by '-1nx'. l = -2n-1x-1 Simplifying l = -2n-1x-1Subproblem 2
Set the factor '(12 + -1lnx)' equal to zero and attempt to solve: Simplifying 12 + -1lnx = 0 Solving 12 + -1lnx = 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 + -1lnx = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1lnx = 0 + -12 -1lnx = 0 + -12 Combine like terms: 0 + -12 = -12 -1lnx = -12 Divide each side by '-1nx'. l = 12n-1x-1 Simplifying l = 12n-1x-1Solution
l = {-2n-1x-1, 12n-1x-1}
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