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Simplifying ln(35 + -1x3) = ln(5 + -1x) (35 * ln + -1x3 * ln) = ln(5 + -1x) (35ln + -1lnx3) = ln(5 + -1x) 35ln + -1lnx3 = (5 * ln + -1x * ln) 35ln + -1lnx3 = (5ln + -1lnx) Solving 35ln + -1lnx3 = 5ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. 35ln + -5ln + -1lnx3 = 5ln + -5ln + -1lnx Combine like terms: 35ln + -5ln = 30ln 30ln + -1lnx3 = 5ln + -5ln + -1lnx Combine like terms: 5ln + -5ln = 0 30ln + -1lnx3 = 0 + -1lnx 30ln + -1lnx3 = -1lnx Add 'lnx' to each side of the equation. 30ln + lnx + -1lnx3 = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 30ln + lnx + -1lnx3 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(30 + x + -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 '(30 + x + -1x3)' equal to zero and attempt to solve: Simplifying 30 + x + -1x3 = 0 Solving 30 + x + -1x3 = 0 Move all terms containing l to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + x + -30 + -1x3 = 0 + -30 Reorder the terms: 30 + -30 + x + -1x3 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + x + -1x3 = 0 + -30 x + -1x3 = 0 + -30 Combine like terms: 0 + -30 = -30 x + -1x3 = -30 Add '-1x' to each side of the equation. x + -1x + -1x3 = -30 + -1x Combine like terms: x + -1x = 0 0 + -1x3 = -30 + -1x -1x3 = -30 + -1x Add 'x3' to each side of the equation. -1x3 + x3 = -30 + -1x + x3 Combine like terms: -1x3 + x3 = 0 0 = -30 + -1x + x3 Simplifying 0 = -30 + -1x + 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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