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Simplifying ln(4x + -7) = ln(x + -4) Reorder the terms: ln(-7 + 4x) = ln(x + -4) (-7 * ln + 4x * ln) = ln(x + -4) (-7ln + 4lnx) = ln(x + -4) Reorder the terms: -7ln + 4lnx = ln(-4 + x) -7ln + 4lnx = (-4 * ln + x * ln) -7ln + 4lnx = (-4ln + lnx) Solving -7ln + 4lnx = -4ln + lnx 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 + lnx Combine like terms: -7ln + 4ln = -3ln -3ln + 4lnx = -4ln + 4ln + lnx Combine like terms: -4ln + 4ln = 0 -3ln + 4lnx = 0 + lnx -3ln + 4lnx = lnx Add '-1lnx' to each side of the equation. -3ln + 4lnx + -1lnx = lnx + -1lnx Combine like terms: 4lnx + -1lnx = 3lnx -3ln + 3lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -3ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-1 + x) = 0 Ignore the factor 3.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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -1x 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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