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