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Simplifying ln(9) = ln(21x + 35) Reorder the terms for easier multiplication: 9ln = ln(21x + 35) Reorder the terms: 9ln = ln(35 + 21x) 9ln = (35 * ln + 21x * ln) 9ln = (35ln + 21lnx) Solving 9ln = 35ln + 21lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-35ln' to each side of the equation. 9ln + -35ln = 35ln + -35ln + 21lnx Combine like terms: 9ln + -35ln = -26ln -26ln = 35ln + -35ln + 21lnx Combine like terms: 35ln + -35ln = 0 -26ln = 0 + 21lnx -26ln = 21lnx Add '-21lnx' to each side of the equation. -26ln + -21lnx = 21lnx + -21lnx Combine like terms: 21lnx + -21lnx = 0 -26ln + -21lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(26 + 21x) = 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 '(26 + 21x)' equal to zero and attempt to solve: Simplifying 26 + 21x = 0 Solving 26 + 21x = 0 Move all terms containing l to the left, all other terms to the right. Add '-26' to each side of the equation. 26 + -26 + 21x = 0 + -26 Combine like terms: 26 + -26 = 0 0 + 21x = 0 + -26 21x = 0 + -26 Combine like terms: 0 + -26 = -26 21x = -26 Add '-21x' to each side of the equation. 21x + -21x = -26 + -21x Combine like terms: 21x + -21x = 0 0 = -26 + -21x Simplifying 0 = -26 + -21x 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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