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Simplifying ln(2x + -3) + ln(x + -2) = 21lnx Reorder the terms: ln(-3 + 2x) + ln(x + -2) = 21lnx (-3 * ln + 2x * ln) + ln(x + -2) = 21lnx (-3ln + 2lnx) + ln(x + -2) = 21lnx Reorder the terms: -3ln + 2lnx + ln(-2 + x) = 21lnx -3ln + 2lnx + (-2 * ln + x * ln) = 21lnx -3ln + 2lnx + (-2ln + lnx) = 21lnx Reorder the terms: -3ln + -2ln + 2lnx + lnx = 21lnx Combine like terms: -3ln + -2ln = -5ln -5ln + 2lnx + lnx = 21lnx Combine like terms: 2lnx + lnx = 3lnx -5ln + 3lnx = 21lnx Solving -5ln + 3lnx = 21lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-21lnx' to each side of the equation. -5ln + 3lnx + -21lnx = 21lnx + -21lnx Combine like terms: 3lnx + -21lnx = -18lnx -5ln + -18lnx = 21lnx + -21lnx Combine like terms: 21lnx + -21lnx = 0 -5ln + -18lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(5 + 18x) = 0 Ignore the factor -1.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 '(5 + 18x)' equal to zero and attempt to solve: Simplifying 5 + 18x = 0 Solving 5 + 18x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 18x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 18x = 0 + -5 18x = 0 + -5 Combine like terms: 0 + -5 = -5 18x = -5 Add '-18x' to each side of the equation. 18x + -18x = -5 + -18x Combine like terms: 18x + -18x = 0 0 = -5 + -18x Simplifying 0 = -5 + -18x 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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