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Simplifying 3xln(5) + -4ln(2) = ln(3) + -1xln(7) Reorder the terms for easier multiplication: 3 * 5lnx + -4ln(2) = ln(3) + -1xln(7) Multiply 3 * 5 15lnx + -4ln(2) = ln(3) + -1xln(7) Reorder the terms for easier multiplication: 15lnx + -4 * 2ln = ln(3) + -1xln(7) Multiply -4 * 2 15lnx + -8ln = ln(3) + -1xln(7) Reorder the terms: -8ln + 15lnx = ln(3) + -1xln(7) Reorder the terms for easier multiplication: -8ln + 15lnx = 3ln + -1xln(7) Reorder the terms for easier multiplication: -8ln + 15lnx = 3ln + -1 * 7lnx Multiply -1 * 7 -8ln + 15lnx = 3ln + -7lnx Solving -8ln + 15lnx = 3ln + -7lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. -8ln + -3ln + 15lnx = 3ln + -3ln + -7lnx Combine like terms: -8ln + -3ln = -11ln -11ln + 15lnx = 3ln + -3ln + -7lnx Combine like terms: 3ln + -3ln = 0 -11ln + 15lnx = 0 + -7lnx -11ln + 15lnx = -7lnx Add '7lnx' to each side of the equation. -11ln + 15lnx + 7lnx = -7lnx + 7lnx Combine like terms: 15lnx + 7lnx = 22lnx -11ln + 22lnx = -7lnx + 7lnx Combine like terms: -7lnx + 7lnx = 0 -11ln + 22lnx = 0 Factor out the Greatest Common Factor (GCF), '11ln'. 11ln(-1 + 2x) = 0 Ignore the factor 11.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 + 2x)' equal to zero and attempt to solve: Simplifying -1 + 2x = 0 Solving -1 + 2x = 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 + 2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x = 0 + 1 2x = 0 + 1 Combine like terms: 0 + 1 = 1 2x = 1 Add '-2x' to each side of the equation. 2x + -2x = 1 + -2x Combine like terms: 2x + -2x = 0 0 = 1 + -2x Simplifying 0 = 1 + -2x 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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