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Simplifying 2ln(5x) = ln(500) Remove parenthesis around (5x) 2ln * 5x = ln(500) Reorder the terms for easier multiplication: 2 * 5ln * x = ln(500) Multiply 2 * 5 10ln * x = ln(500) Multiply ln * x 10lnx = ln(500) Reorder the terms for easier multiplication: 10lnx = 500ln Solving 10lnx = 500ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-500ln' to each side of the equation. -500ln + 10lnx = 500ln + -500ln Combine like terms: 500ln + -500ln = 0 -500ln + 10lnx = 0 Factor out the Greatest Common Factor (GCF), '10ln'. 10ln(-50 + x) = 0 Ignore the factor 10.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 '(-50 + x)' equal to zero and attempt to solve: Simplifying -50 + x = 0 Solving -50 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 0 + 50 Combine like terms: -50 + 50 = 0 0 + x = 0 + 50 x = 0 + 50 Combine like terms: 0 + 50 = 50 x = 50 Add '-1x' to each side of the equation. x + -1x = 50 + -1x Combine like terms: x + -1x = 0 0 = 50 + -1x Simplifying 0 = 50 + -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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