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Simplifying 6lnx2 + -1lnx10 = ln(4x + 21) Reorder the terms: 6lnx2 + -1lnx10 = ln(21 + 4x) 6lnx2 + -1lnx10 = (21 * ln + 4x * ln) 6lnx2 + -1lnx10 = (21ln + 4lnx) Solving 6lnx2 + -1lnx10 = 21ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-21ln' to each side of the equation. 6lnx2 + -21ln + -1lnx10 = 21ln + -21ln + 4lnx Reorder the terms: -21ln + 6lnx2 + -1lnx10 = 21ln + -21ln + 4lnx Combine like terms: 21ln + -21ln = 0 -21ln + 6lnx2 + -1lnx10 = 0 + 4lnx -21ln + 6lnx2 + -1lnx10 = 4lnx Add '-4lnx' to each side of the equation. -21ln + 6lnx2 + -4lnx + -1lnx10 = 4lnx + -4lnx Reorder the terms: -21ln + -4lnx + 6lnx2 + -1lnx10 = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 -21ln + -4lnx + 6lnx2 + -1lnx10 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-21 + -4x + 6x2 + -1x10) = 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 '(-21 + -4x + 6x2 + -1x10)' equal to zero and attempt to solve: Simplifying -21 + -4x + 6x2 + -1x10 = 0 Solving -21 + -4x + 6x2 + -1x10 = 0 Move all terms containing l to the left, all other terms to the right. Add '21' to each side of the equation. -21 + -4x + 6x2 + 21 + -1x10 = 0 + 21 Reorder the terms: -21 + 21 + -4x + 6x2 + -1x10 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -4x + 6x2 + -1x10 = 0 + 21 -4x + 6x2 + -1x10 = 0 + 21 Combine like terms: 0 + 21 = 21 -4x + 6x2 + -1x10 = 21 Add '4x' to each side of the equation. -4x + 6x2 + 4x + -1x10 = 21 + 4x Reorder the terms: -4x + 4x + 6x2 + -1x10 = 21 + 4x Combine like terms: -4x + 4x = 0 0 + 6x2 + -1x10 = 21 + 4x 6x2 + -1x10 = 21 + 4x Add '-6x2' to each side of the equation. 6x2 + -6x2 + -1x10 = 21 + 4x + -6x2 Combine like terms: 6x2 + -6x2 = 0 0 + -1x10 = 21 + 4x + -6x2 -1x10 = 21 + 4x + -6x2 Add 'x10' to each side of the equation. -1x10 + x10 = 21 + 4x + -6x2 + x10 Combine like terms: -1x10 + x10 = 0 0 = 21 + 4x + -6x2 + x10 Simplifying 0 = 21 + 4x + -6x2 + x10 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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