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Simplifying ln(3x + -4) = ln8 + -1ln(x + -2) Reorder the terms: ln(-4 + 3x) = ln8 + -1ln(x + -2) (-4 * ln + 3x * ln) = ln8 + -1ln(x + -2) (-4ln + 3lnx) = ln8 + -1ln(x + -2) Reorder the terms: -4ln + 3lnx = ln8 + -1ln(-2 + x) -4ln + 3lnx = ln8 + (-2 * -1ln + x * -1ln) -4ln + 3lnx = ln8 + (2ln + -1lnx) Reorder the terms: -4ln + 3lnx = 2ln + -1lnx + ln8 Solving -4ln + 3lnx = 2ln + -1lnx + ln8 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. -4ln + -2ln + 3lnx = 2ln + -1lnx + -2ln + ln8 Combine like terms: -4ln + -2ln = -6ln -6ln + 3lnx = 2ln + -1lnx + -2ln + ln8 Reorder the terms: -6ln + 3lnx = 2ln + -2ln + -1lnx + ln8 Combine like terms: 2ln + -2ln = 0 -6ln + 3lnx = 0 + -1lnx + ln8 -6ln + 3lnx = -1lnx + ln8 Add 'lnx' to each side of the equation. -6ln + 3lnx + lnx = -1lnx + lnx + ln8 Combine like terms: 3lnx + lnx = 4lnx -6ln + 4lnx = -1lnx + lnx + ln8 Combine like terms: -1lnx + lnx = 0 -6ln + 4lnx = 0 + ln8 -6ln + 4lnx = ln8 Add '-1ln8' to each side of the equation. -6ln + 4lnx + -1ln8 = ln8 + -1ln8 Combine like terms: ln8 + -1ln8 = 0 -6ln + 4lnx + -1ln8 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-6 + 4x + -1n7) = 0Subproblem 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 '(-6 + 4x + -1n7)' equal to zero and attempt to solve: Simplifying -6 + 4x + -1n7 = 0 Reorder the terms: -6 + -1n7 + 4x = 0 Solving -6 + -1n7 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '6' to each side of the equation. -6 + -1n7 + 6 + 4x = 0 + 6 Reorder the terms: -6 + 6 + -1n7 + 4x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1n7 + 4x = 0 + 6 -1n7 + 4x = 0 + 6 Combine like terms: 0 + 6 = 6 -1n7 + 4x = 6 Add 'n7' to each side of the equation. -1n7 + n7 + 4x = 6 + n7 Combine like terms: -1n7 + n7 = 0 0 + 4x = 6 + n7 4x = 6 + n7 Add '-4x' to each side of the equation. 4x + -4x = 6 + n7 + -4x Combine like terms: 4x + -4x = 0 0 = 6 + n7 + -4x Simplifying 0 = 6 + n7 + -4x 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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