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Simplifying ln(3x2) + -1ln(x) = ln(15) Remove parenthesis around (3x2) ln * 3x2 + -1ln(x) = ln(15) Reorder the terms for easier multiplication: 3ln * x2 + -1ln(x) = ln(15) Multiply ln * x2 3lnx2 + -1ln(x) = ln(15) Multiply ln * x 3lnx2 + -1lnx = ln(15) Reorder the terms: -1lnx + 3lnx2 = ln(15) Reorder the terms for easier multiplication: -1lnx + 3lnx2 = 15ln Solving -1lnx + 3lnx2 = 15ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-15ln' to each side of the equation. -1lnx + -15ln + 3lnx2 = 15ln + -15ln Reorder the terms: -15ln + -1lnx + 3lnx2 = 15ln + -15ln Combine like terms: 15ln + -15ln = 0 -15ln + -1lnx + 3lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-15 + -1x + 3x2) = 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 '(-15 + -1x + 3x2)' equal to zero and attempt to solve: Simplifying -15 + -1x + 3x2 = 0 Solving -15 + -1x + 3x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '15' to each side of the equation. -15 + -1x + 15 + 3x2 = 0 + 15 Reorder the terms: -15 + 15 + -1x + 3x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x + 3x2 = 0 + 15 -1x + 3x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -1x + 3x2 = 15 Add 'x' to each side of the equation. -1x + x + 3x2 = 15 + x Combine like terms: -1x + x = 0 0 + 3x2 = 15 + x 3x2 = 15 + x Add '-3x2' to each side of the equation. 3x2 + -3x2 = 15 + x + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 = 15 + x + -3x2 Simplifying 0 = 15 + x + -3x2 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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