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Simplifying ln(4x2 + -8x + -30) = 2ln(2x) Reorder the terms: ln(-30 + -8x + 4x2) = 2ln(2x) (-30 * ln + -8x * ln + 4x2 * ln) = 2ln(2x) (-30ln + -8lnx + 4lnx2) = 2ln(2x) Remove parenthesis around (2x) -30ln + -8lnx + 4lnx2 = 2ln * 2x Reorder the terms for easier multiplication: -30ln + -8lnx + 4lnx2 = 2 * 2ln * x Multiply 2 * 2 -30ln + -8lnx + 4lnx2 = 4ln * x Multiply ln * x -30ln + -8lnx + 4lnx2 = 4lnx Solving -30ln + -8lnx + 4lnx2 = 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4lnx' to each side of the equation. -30ln + -8lnx + -4lnx + 4lnx2 = 4lnx + -4lnx Combine like terms: -8lnx + -4lnx = -12lnx -30ln + -12lnx + 4lnx2 = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 -30ln + -12lnx + 4lnx2 = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-15 + -6x + 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 + -6x + 2x2)' equal to zero and attempt to solve: Simplifying -15 + -6x + 2x2 = 0 Solving -15 + -6x + 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 + -6x + 15 + 2x2 = 0 + 15 Reorder the terms: -15 + 15 + -6x + 2x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -6x + 2x2 = 0 + 15 -6x + 2x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -6x + 2x2 = 15 Add '6x' to each side of the equation. -6x + 6x + 2x2 = 15 + 6x Combine like terms: -6x + 6x = 0 0 + 2x2 = 15 + 6x 2x2 = 15 + 6x Add '-2x2' to each side of the equation. 2x2 + -2x2 = 15 + 6x + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 = 15 + 6x + -2x2 Simplifying 0 = 15 + 6x + -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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