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Simplifying 3ln(x) + ln(x2) = ln(32) Multiply ln * x 3lnx + ln(x2) = ln(32) Multiply ln * x2 3lnx + lnx2 = ln(32) Reorder the terms for easier multiplication: 3lnx + lnx2 = 32ln Solving 3lnx + lnx2 = 32ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-32ln' to each side of the equation. 3lnx + -32ln + lnx2 = 32ln + -32ln Reorder the terms: -32ln + 3lnx + lnx2 = 32ln + -32ln Combine like terms: 32ln + -32ln = 0 -32ln + 3lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-32 + 3x + x2) = 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 '(-32 + 3x + x2)' equal to zero and attempt to solve: Simplifying -32 + 3x + x2 = 0 Solving -32 + 3x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 3x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 3x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 3x + x2 = 0 + 32 3x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 3x + x2 = 32 Add '-3x' to each side of the equation. 3x + -3x + x2 = 32 + -3x Combine like terms: 3x + -3x = 0 0 + x2 = 32 + -3x x2 = 32 + -3x Add '-1x2' to each side of the equation. x2 + -1x2 = 32 + -3x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = 32 + -3x + -1x2 Simplifying 0 = 32 + -3x + -1x2 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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