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