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Simplifying ln(35 + -1x3) = 3ln(5 + -1x) (35 * ln + -1x3 * ln) = 3ln(5 + -1x) (35ln + -1lnx3) = 3ln(5 + -1x) 35ln + -1lnx3 = (5 * 3ln + -1x * 3ln) 35ln + -1lnx3 = (15ln + -3lnx) Solving 35ln + -1lnx3 = 15ln + -3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-15ln' to each side of the equation. 35ln + -15ln + -1lnx3 = 15ln + -15ln + -3lnx Combine like terms: 35ln + -15ln = 20ln 20ln + -1lnx3 = 15ln + -15ln + -3lnx Combine like terms: 15ln + -15ln = 0 20ln + -1lnx3 = 0 + -3lnx 20ln + -1lnx3 = -3lnx Add '3lnx' to each side of the equation. 20ln + 3lnx + -1lnx3 = -3lnx + 3lnx Combine like terms: -3lnx + 3lnx = 0 20ln + 3lnx + -1lnx3 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(20 + 3x + -1x3) = 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 '(20 + 3x + -1x3)' equal to zero and attempt to solve: Simplifying 20 + 3x + -1x3 = 0 Solving 20 + 3x + -1x3 = 0 Move all terms containing l to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + 3x + -20 + -1x3 = 0 + -20 Reorder the terms: 20 + -20 + 3x + -1x3 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 3x + -1x3 = 0 + -20 3x + -1x3 = 0 + -20 Combine like terms: 0 + -20 = -20 3x + -1x3 = -20 Add '-3x' to each side of the equation. 3x + -3x + -1x3 = -20 + -3x Combine like terms: 3x + -3x = 0 0 + -1x3 = -20 + -3x -1x3 = -20 + -3x Add 'x3' to each side of the equation. -1x3 + x3 = -20 + -3x + x3 Combine like terms: -1x3 + x3 = 0 0 = -20 + -3x + x3 Simplifying 0 = -20 + -3x + x3 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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