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Simplifying ln(11x) = ln(x2 + 28) Remove parenthesis around (11x) ln * 11x = ln(x2 + 28) Reorder the terms for easier multiplication: 11ln * x = ln(x2 + 28) Multiply ln * x 11lnx = ln(x2 + 28) Reorder the terms: 11lnx = ln(28 + x2) 11lnx = (28 * ln + x2 * ln) 11lnx = (28ln + lnx2) Solving 11lnx = 28ln + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-28ln' to each side of the equation. -28ln + 11lnx = 28ln + -28ln + lnx2 Combine like terms: 28ln + -28ln = 0 -28ln + 11lnx = 0 + lnx2 -28ln + 11lnx = lnx2 Add '-1lnx2' to each side of the equation. -28ln + 11lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -28ln + 11lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-28 + 11x + -1x2) = 0 Factor a trinomial. ln((-7 + x)(4 + -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 '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Add '-1x' to each side of the equation. x + -1x = 7 + -1x Combine like terms: x + -1x = 0 0 = 7 + -1x Simplifying 0 = 7 + -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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + 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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