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Simplifying ln(4x2) + -1ln(10x) = ln(30) Remove parenthesis around (4x2) ln * 4x2 + -1ln(10x) = ln(30) Reorder the terms for easier multiplication: 4ln * x2 + -1ln(10x) = ln(30) Multiply ln * x2 4lnx2 + -1ln(10x) = ln(30) Remove parenthesis around (10x) 4lnx2 + -1ln * 10x = ln(30) Reorder the terms for easier multiplication: 4lnx2 + -1 * 10ln * x = ln(30) Multiply -1 * 10 4lnx2 + -10ln * x = ln(30) Multiply ln * x 4lnx2 + -10lnx = ln(30) Reorder the terms: -10lnx + 4lnx2 = ln(30) Reorder the terms for easier multiplication: -10lnx + 4lnx2 = 30ln Solving -10lnx + 4lnx2 = 30ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-30ln' to each side of the equation. -10lnx + -30ln + 4lnx2 = 30ln + -30ln Reorder the terms: -30ln + -10lnx + 4lnx2 = 30ln + -30ln Combine like terms: 30ln + -30ln = 0 -30ln + -10lnx + 4lnx2 = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-15 + -5x + 2x2) = 0 Ignore the factor 2.Subproblem 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 + -5x + 2x2)' equal to zero and attempt to solve: Simplifying -15 + -5x + 2x2 = 0 Solving -15 + -5x + 2x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '15' to each side of the equation. -15 + -5x + 15 + 2x2 = 0 + 15 Reorder the terms: -15 + 15 + -5x + 2x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -5x + 2x2 = 0 + 15 -5x + 2x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -5x + 2x2 = 15 Add '5x' to each side of the equation. -5x + 5x + 2x2 = 15 + 5x Combine like terms: -5x + 5x = 0 0 + 2x2 = 15 + 5x 2x2 = 15 + 5x Add '-2x2' to each side of the equation. 2x2 + -2x2 = 15 + 5x + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 = 15 + 5x + -2x2 Simplifying 0 = 15 + 5x + -2x2 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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