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Simplifying ln(4x + -4) + ln(2x) = 2lnx Reorder the terms: ln(-4 + 4x) + ln(2x) = 2lnx (-4 * ln + 4x * ln) + ln(2x) = 2lnx (-4ln + 4lnx) + ln(2x) = 2lnx Remove parenthesis around (2x) -4ln + 4lnx + ln * 2x = 2lnx Reorder the terms for easier multiplication: -4ln + 4lnx + 2ln * x = 2lnx Multiply ln * x -4ln + 4lnx + 2lnx = 2lnx Combine like terms: 4lnx + 2lnx = 6lnx -4ln + 6lnx = 2lnx Solving -4ln + 6lnx = 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. -4ln + 6lnx + -2lnx = 2lnx + -2lnx Combine like terms: 6lnx + -2lnx = 4lnx -4ln + 4lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 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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