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Simplifying 6ln(x) + -1ln(x4) = ln(6x + 40) Multiply ln * x 6lnx + -1ln(x4) = ln(6x + 40) Multiply ln * x4 6lnx + -1lnx4 = ln(6x + 40) Reorder the terms: 6lnx + -1lnx4 = ln(40 + 6x) 6lnx + -1lnx4 = (40 * ln + 6x * ln) 6lnx + -1lnx4 = (40ln + 6lnx) Add '-6lnx' to each side of the equation. 6lnx + -6lnx + -1lnx4 = 40ln + 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 0 + -1lnx4 = 40ln + 6lnx + -6lnx -1lnx4 = 40ln + 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 -1lnx4 = 40ln + 0 -1lnx4 = 40ln Solving -1lnx4 = 40ln 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. -40ln + -1lnx4 = 40ln + -40ln Combine like terms: 40ln + -40ln = 0 -40ln + -1lnx4 = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(40 + x4) = 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 '(40 + x4)' equal to zero and attempt to solve: Simplifying 40 + x4 = 0 Solving 40 + x4 = 0 Move all terms containing l to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x4 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + x4 = 0 + -40 x4 = 0 + -40 Combine like terms: 0 + -40 = -40 x4 = -40 Add '-1x4' to each side of the equation. x4 + -1x4 = -40 + -1x4 Combine like terms: x4 + -1x4 = 0 0 = -40 + -1x4 Simplifying 0 = -40 + -1x4 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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