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Simplifying ln(5000) = 6ln(x) Reorder the terms for easier multiplication: 5000ln = 6ln(x) Multiply ln * x 5000ln = 6lnx Solving 5000ln = 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6lnx' to each side of the equation. 5000ln + -6lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 5000ln + -6lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(2500 + -3x) = 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 '(2500 + -3x)' equal to zero and attempt to solve: Simplifying 2500 + -3x = 0 Solving 2500 + -3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2500' to each side of the equation. 2500 + -2500 + -3x = 0 + -2500 Combine like terms: 2500 + -2500 = 0 0 + -3x = 0 + -2500 -3x = 0 + -2500 Combine like terms: 0 + -2500 = -2500 -3x = -2500 Add '3x' to each side of the equation. -3x + 3x = -2500 + 3x Combine like terms: -3x + 3x = 0 0 = -2500 + 3x Simplifying 0 = -2500 + 3x 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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