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Simplifying ln(4x + -7) = ln(x2 + -4) Reorder the terms: ln(-7 + 4x) = ln(x2 + -4) (-7 * ln + 4x * ln) = ln(x2 + -4) (-7ln + 4lnx) = ln(x2 + -4) Reorder the terms: -7ln + 4lnx = ln(-4 + x2) -7ln + 4lnx = (-4 * ln + x2 * ln) -7ln + 4lnx = (-4ln + lnx2) Solving -7ln + 4lnx = -4ln + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '4ln' to each side of the equation. -7ln + 4ln + 4lnx = -4ln + 4ln + lnx2 Combine like terms: -7ln + 4ln = -3ln -3ln + 4lnx = -4ln + 4ln + lnx2 Combine like terms: -4ln + 4ln = 0 -3ln + 4lnx = 0 + lnx2 -3ln + 4lnx = lnx2 Add '-1lnx2' to each side of the equation. -3ln + 4lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -3ln + 4lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-3 + 4x + -1x2) = 0 Factor a trinomial. ln((-3 + 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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -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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