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Simplifying ln(6x) = ln((x2) + 5) Remove parenthesis around (6x) ln * 6x = ln((x2) + 5) Reorder the terms for easier multiplication: 6ln * x = ln((x2) + 5) Multiply ln * x 6lnx = ln((x2) + 5) 6lnx = ln(x2 + 5) Reorder the terms: 6lnx = ln(5 + x2) 6lnx = (5 * ln + x2 * ln) 6lnx = (5ln + lnx2) Solving 6lnx = 5ln + lnx2 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. -5ln + 6lnx = 5ln + -5ln + lnx2 Combine like terms: 5ln + -5ln = 0 -5ln + 6lnx = 0 + lnx2 -5ln + 6lnx = lnx2 Add '-1lnx2' to each side of the equation. -5ln + 6lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -5ln + 6lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-5 + 6x + -1x2) = 0 Factor a trinomial. ln((-5 + x)(1 + -1x)) = 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 '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Add '-1x' to each side of the equation. x + -1x = 5 + -1x Combine like terms: x + -1x = 0 0 = 5 + -1x Simplifying 0 = 5 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x 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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