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Simplifying 2ln(5x) = ln(15x + -2) Remove parenthesis around (5x) 2ln * 5x = ln(15x + -2) Reorder the terms for easier multiplication: 2 * 5ln * x = ln(15x + -2) Multiply 2 * 5 10ln * x = ln(15x + -2) Multiply ln * x 10lnx = ln(15x + -2) Reorder the terms: 10lnx = ln(-2 + 15x) 10lnx = (-2 * ln + 15x * ln) 10lnx = (-2ln + 15lnx) Solving 10lnx = -2ln + 15lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2ln' to each side of the equation. 2ln + 10lnx = -2ln + 2ln + 15lnx Combine like terms: -2ln + 2ln = 0 2ln + 10lnx = 0 + 15lnx 2ln + 10lnx = 15lnx Add '-15lnx' to each side of the equation. 2ln + 10lnx + -15lnx = 15lnx + -15lnx Combine like terms: 10lnx + -15lnx = -5lnx 2ln + -5lnx = 15lnx + -15lnx Combine like terms: 15lnx + -15lnx = 0 2ln + -5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(2 + -5x) = 0Subproblem 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 '(2 + -5x)' equal to zero and attempt to solve: Simplifying 2 + -5x = 0 Solving 2 + -5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5x = 0 + -2 -5x = 0 + -2 Combine like terms: 0 + -2 = -2 -5x = -2 Add '5x' to each side of the equation. -5x + 5x = -2 + 5x Combine like terms: -5x + 5x = 0 0 = -2 + 5x Simplifying 0 = -2 + 5x 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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