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Simplifying 8lnx + -1ln(x6) = ln(6x + 40) Multiply ln * x6 8lnx + -1lnx6 = ln(6x + 40) Reorder the terms: 8lnx + -1lnx6 = ln(40 + 6x) 8lnx + -1lnx6 = (40 * ln + 6x * ln) 8lnx + -1lnx6 = (40ln + 6lnx) Solving 8lnx + -1lnx6 = 40ln + 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-40ln' to each side of the equation. 8lnx + -40ln + -1lnx6 = 40ln + -40ln + 6lnx Reorder the terms: -40ln + 8lnx + -1lnx6 = 40ln + -40ln + 6lnx Combine like terms: 40ln + -40ln = 0 -40ln + 8lnx + -1lnx6 = 0 + 6lnx -40ln + 8lnx + -1lnx6 = 6lnx Add '-6lnx' to each side of the equation. -40ln + 8lnx + -6lnx + -1lnx6 = 6lnx + -6lnx Combine like terms: 8lnx + -6lnx = 2lnx -40ln + 2lnx + -1lnx6 = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 -40ln + 2lnx + -1lnx6 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-40 + 2x + -1x6) = 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 '(-40 + 2x + -1x6)' equal to zero and attempt to solve: Simplifying -40 + 2x + -1x6 = 0 Solving -40 + 2x + -1x6 = 0 Move all terms containing l to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 2x + 40 + -1x6 = 0 + 40 Reorder the terms: -40 + 40 + 2x + -1x6 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 2x + -1x6 = 0 + 40 2x + -1x6 = 0 + 40 Combine like terms: 0 + 40 = 40 2x + -1x6 = 40 Add '-2x' to each side of the equation. 2x + -2x + -1x6 = 40 + -2x Combine like terms: 2x + -2x = 0 0 + -1x6 = 40 + -2x -1x6 = 40 + -2x Add 'x6' to each side of the equation. -1x6 + x6 = 40 + -2x + x6 Combine like terms: -1x6 + x6 = 0 0 = 40 + -2x + x6 Simplifying 0 = 40 + -2x + x6 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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