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Simplifying lnx(lnx + 8) = 9 Reorder the terms: lnx(8 + lnx) = 9 (8 * lnx + lnx * lnx) = 9 (8lnx + l2n2x2) = 9 Solving 8lnx + l2n2x2 = 9 Solving for variable 'l'. Reorder the terms: -9 + 8lnx + l2n2x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 8lnx + l2n2x2 = 0 Factor a trinomial. (-9 + -1lnx)(1 + -1lnx) = 0Subproblem 1
Set the factor '(-9 + -1lnx)' equal to zero and attempt to solve: Simplifying -9 + -1lnx = 0 Solving -9 + -1lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1lnx = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1lnx = 0 + 9 -1lnx = 0 + 9 Combine like terms: 0 + 9 = 9 -1lnx = 9 Divide each side by '-1nx'. l = -9n-1x-1 Simplifying l = -9n-1x-1Subproblem 2
Set the factor '(1 + -1lnx)' equal to zero and attempt to solve: Simplifying 1 + -1lnx = 0 Solving 1 + -1lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1lnx = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1lnx = 0 + -1 -1lnx = 0 + -1 Combine like terms: 0 + -1 = -1 -1lnx = -1 Divide each side by '-1nx'. l = n-1x-1 Simplifying l = n-1x-1Solution
l = {-9n-1x-1, n-1x-1}
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