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