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Simplifying ln(8x + 3) + lnx = lne Reorder the terms: ln(3 + 8x) + lnx = lne (3 * ln + 8x * ln) + lnx = lne (3ln + 8lnx) + lnx = lne Combine like terms: 8lnx + lnx = 9lnx 3ln + 9lnx = lne Solving 3ln + 9lnx = eln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1eln' to each side of the equation. 3ln + -1eln + 9lnx = eln + -1eln Reorder the terms: -1eln + 3ln + 9lnx = eln + -1eln Combine like terms: eln + -1eln = 0 -1eln + 3ln + 9lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-1e + 3 + 9x) = 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 '(-1e + 3 + 9x)' equal to zero and attempt to solve: Simplifying -1e + 3 + 9x = 0 Reorder the terms: 3 + -1e + 9x = 0 Solving 3 + -1e + 9x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -1e + -3 + 9x = 0 + -3 Reorder the terms: 3 + -3 + -1e + 9x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1e + 9x = 0 + -3 -1e + 9x = 0 + -3 Combine like terms: 0 + -3 = -3 -1e + 9x = -3 Add 'e' to each side of the equation. -1e + e + 9x = -3 + e Combine like terms: -1e + e = 0 0 + 9x = -3 + e 9x = -3 + e Add '-9x' to each side of the equation. 9x + -9x = -3 + e + -9x Combine like terms: 9x + -9x = 0 0 = -3 + e + -9x Simplifying 0 = -3 + e + -9x 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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