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Simplifying ln(6x + -8) + ln(8x) = 2lnx Reorder the terms: ln(-8 + 6x) + ln(8x) = 2lnx (-8 * ln + 6x * ln) + ln(8x) = 2lnx (-8ln + 6lnx) + ln(8x) = 2lnx Remove parenthesis around (8x) -8ln + 6lnx + ln * 8x = 2lnx Reorder the terms for easier multiplication: -8ln + 6lnx + 8ln * x = 2lnx Multiply ln * x -8ln + 6lnx + 8lnx = 2lnx Combine like terms: 6lnx + 8lnx = 14lnx -8ln + 14lnx = 2lnx Solving -8ln + 14lnx = 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. -8ln + 14lnx + -2lnx = 2lnx + -2lnx Combine like terms: 14lnx + -2lnx = 12lnx -8ln + 12lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -8ln + 12lnx = 0 Factor out the Greatest Common Factor (GCF), '4ln'. 4ln(-2 + 3x) = 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 '(-2 + 3x)' equal to zero and attempt to solve: Simplifying -2 + 3x = 0 Solving -2 + 3x = 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 + 3x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3x = 0 + 2 3x = 0 + 2 Combine like terms: 0 + 2 = 2 3x = 2 Add '-3x' to each side of the equation. 3x + -3x = 2 + -3x Combine like terms: 3x + -3x = 0 0 = 2 + -3x Simplifying 0 = 2 + -3x 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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