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