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Simplifying ln(x + -2) + ln(x + 4) = ln * 7 Reorder the terms: ln(-2 + x) + ln(x + 4) = ln * 7 (-2 * ln + x * ln) + ln(x + 4) = ln * 7 (-2ln + lnx) + ln(x + 4) = ln * 7 Reorder the terms: -2ln + lnx + ln(4 + x) = ln * 7 -2ln + lnx + (4 * ln + x * ln) = ln * 7 -2ln + lnx + (4ln + lnx) = ln * 7 Reorder the terms: -2ln + 4ln + lnx + lnx = ln * 7 Combine like terms: -2ln + 4ln = 2ln 2ln + lnx + lnx = ln * 7 Combine like terms: lnx + lnx = 2lnx 2ln + 2lnx = ln * 7 Reorder the terms for easier multiplication: 2ln + 2lnx = 7ln Solving 2ln + 2lnx = 7ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7ln' to each side of the equation. 2ln + -7ln + 2lnx = 7ln + -7ln Combine like terms: 2ln + -7ln = -5ln -5ln + 2lnx = 7ln + -7ln Combine like terms: 7ln + -7ln = 0 -5ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-5 + 2x) = 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 + 2x)' equal to zero and attempt to solve: Simplifying -5 + 2x = 0 Solving -5 + 2x = 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 + 2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x = 0 + 5 2x = 0 + 5 Combine like terms: 0 + 5 = 5 2x = 5 Add '-2x' to each side of the equation. 2x + -2x = 5 + -2x Combine like terms: 2x + -2x = 0 0 = 5 + -2x Simplifying 0 = 5 + -2x 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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