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Simplifying ln(5x + -8) + ln(2) = 2ln(x) Reorder the terms: ln(-8 + 5x) + ln(2) = 2ln(x) (-8 * ln + 5x * ln) + ln(2) = 2ln(x) (-8ln + 5lnx) + ln(2) = 2ln(x) Reorder the terms for easier multiplication: -8ln + 5lnx + 2ln = 2ln(x) Reorder the terms: -8ln + 2ln + 5lnx = 2ln(x) Combine like terms: -8ln + 2ln = -6ln -6ln + 5lnx = 2ln(x) Multiply ln * x -6ln + 5lnx = 2lnx Solving -6ln + 5lnx = 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2lnx' to each side of the equation. -6ln + 5lnx + -2lnx = 2lnx + -2lnx Combine like terms: 5lnx + -2lnx = 3lnx -6ln + 3lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -6ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-2 + x) = 0 Ignore the factor 3.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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -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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