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Simplifying ln(x) = ln(3) + ln(5) + -1ln(x) Multiply ln * x lnx = ln(3) + ln(5) + -1ln(x) Reorder the terms for easier multiplication: lnx = 3ln + ln(5) + -1ln(x) Reorder the terms for easier multiplication: lnx = 3ln + 5ln + -1ln(x) Multiply ln * x lnx = 3ln + 5ln + -1lnx Combine like terms: 3ln + 5ln = 8ln lnx = 8ln + -1lnx Solving lnx = 8ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. -8ln + lnx = 8ln + -8ln + -1lnx Combine like terms: 8ln + -8ln = 0 -8ln + lnx = 0 + -1lnx -8ln + lnx = -1lnx Add 'lnx' to each side of the equation. -8ln + lnx + lnx = -1lnx + lnx Combine like terms: lnx + lnx = 2lnx -8ln + 2lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -8ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-4 + x) = 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 '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Add '-1x' to each side of the equation. x + -1x = 4 + -1x Combine like terms: x + -1x = 0 0 = 4 + -1x Simplifying 0 = 4 + -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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