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Simplifying ln((4x2) + -4x) + -1ln(2x) = ln(8x + -2) + ln(2) Reorder the terms: ln(-4x + (4x2)) + -1ln(2x) = ln(8x + -2) + ln(2) (-4x * ln + (4x2) * ln) + -1ln(2x) = ln(8x + -2) + ln(2) (-4lnx + 4lnx2) + -1ln(2x) = ln(8x + -2) + ln(2) Remove parenthesis around (2x) -4lnx + 4lnx2 + -1ln * 2x = ln(8x + -2) + ln(2) Reorder the terms for easier multiplication: -4lnx + 4lnx2 + -1 * 2ln * x = ln(8x + -2) + ln(2) Multiply -1 * 2 -4lnx + 4lnx2 + -2ln * x = ln(8x + -2) + ln(2) Multiply ln * x -4lnx + 4lnx2 + -2lnx = ln(8x + -2) + ln(2) Reorder the terms: -4lnx + -2lnx + 4lnx2 = ln(8x + -2) + ln(2) Combine like terms: -4lnx + -2lnx = -6lnx -6lnx + 4lnx2 = ln(8x + -2) + ln(2) Reorder the terms: -6lnx + 4lnx2 = ln(-2 + 8x) + ln(2) -6lnx + 4lnx2 = (-2 * ln + 8x * ln) + ln(2) -6lnx + 4lnx2 = (-2ln + 8lnx) + ln(2) Reorder the terms for easier multiplication: -6lnx + 4lnx2 = -2ln + 8lnx + 2ln Reorder the terms: -6lnx + 4lnx2 = -2ln + 2ln + 8lnx Combine like terms: -2ln + 2ln = 0 -6lnx + 4lnx2 = 0 + 8lnx -6lnx + 4lnx2 = 8lnx Solving -6lnx + 4lnx2 = 8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8lnx' to each side of the equation. -6lnx + -8lnx + 4lnx2 = 8lnx + -8lnx Combine like terms: -6lnx + -8lnx = -14lnx -14lnx + 4lnx2 = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 -14lnx + 4lnx2 = 0 Factor out the Greatest Common Factor (GCF), '2lnx'. 2lnx(-7 + 2x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'lnx' equal to zero and attempt to solve: Simplifying lnx = 0 Solving lnx = 0 Move all terms containing l to the left, all other terms to the right. Simplifying lnx = 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 '(-7 + 2x)' equal to zero and attempt to solve: Simplifying -7 + 2x = 0 Solving -7 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2x = 0 + 7 2x = 0 + 7 Combine like terms: 0 + 7 = 7 2x = 7 Add '-2x' to each side of the equation. 2x + -2x = 7 + -2x Combine like terms: 2x + -2x = 0 0 = 7 + -2x Simplifying 0 = 7 + -2x 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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