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Simplifying xln(15) + -1xln(5) = 2ln(5) Reorder the terms for easier multiplication: 15lnx + -1xln(5) = 2ln(5) Reorder the terms for easier multiplication: 15lnx + -1 * 5lnx = 2ln(5) Multiply -1 * 5 15lnx + -5lnx = 2ln(5) Combine like terms: 15lnx + -5lnx = 10lnx 10lnx = 2ln(5) Reorder the terms for easier multiplication: 10lnx = 2 * 5ln Multiply 2 * 5 10lnx = 10ln Solving 10lnx = 10ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. -10ln + 10lnx = 10ln + -10ln Combine like terms: 10ln + -10ln = 0 -10ln + 10lnx = 0 Factor out the Greatest Common Factor (GCF), '10ln'. 10ln(-1 + 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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -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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