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Simplifying 5ln(y) + -5ln(y + 0.2) = ln(x) Multiply ln * y 5lny + -5ln(y + 0.2) = ln(x) Reorder the terms: 5lny + -5ln(0.2 + y) = ln(x) 5lny + (0.2 * -5ln + y * -5ln) = ln(x) 5lny + (-1ln + -5lny) = ln(x) Reorder the terms: -1ln + 5lny + -5lny = ln(x) Combine like terms: 5lny + -5lny = 0 -1ln + 0 = ln(x) -1ln = ln(x) Multiply ln * x -1ln = lnx Solving -1ln = lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnx' to each side of the equation. -1ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -1ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(1 + x) = 0 Ignore the factor -1.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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