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Simplifying lnx + ln(x + -6) + ln(x + -3) = ln(4x) Reorder the terms: lnx + ln(-6 + x) + ln(x + -3) = ln(4x) lnx + (-6 * ln + x * ln) + ln(x + -3) = ln(4x) lnx + (-6ln + lnx) + ln(x + -3) = ln(4x) Reorder the terms: lnx + -6ln + lnx + ln(-3 + x) = ln(4x) lnx + -6ln + lnx + (-3 * ln + x * ln) = ln(4x) lnx + -6ln + lnx + (-3ln + lnx) = ln(4x) Reorder the terms: -6ln + -3ln + lnx + lnx + lnx = ln(4x) Combine like terms: -6ln + -3ln = -9ln -9ln + lnx + lnx + lnx = ln(4x) Combine like terms: lnx + lnx = 2lnx -9ln + 2lnx + lnx = ln(4x) Combine like terms: 2lnx + lnx = 3lnx -9ln + 3lnx = ln(4x) Remove parenthesis around (4x) -9ln + 3lnx = ln * 4x Reorder the terms for easier multiplication: -9ln + 3lnx = 4ln * x Multiply ln * x -9ln + 3lnx = 4lnx Solving -9ln + 3lnx = 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4lnx' to each side of the equation. -9ln + 3lnx + -4lnx = 4lnx + -4lnx Combine like terms: 3lnx + -4lnx = -1lnx -9ln + -1lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 -9ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(9 + x) = 0 Ignore the factor -1.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 '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Add '-1x' to each side of the equation. x + -1x = -9 + -1x Combine like terms: x + -1x = 0 0 = -9 + -1x Simplifying 0 = -9 + -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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