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Simplifying ln(x + 6) + ln(x + -3) = ln(5) + ln(2) Reorder the terms: ln(6 + x) + ln(x + -3) = ln(5) + ln(2) (6 * ln + x * ln) + ln(x + -3) = ln(5) + ln(2) (6ln + lnx) + ln(x + -3) = ln(5) + ln(2) Reorder the terms: 6ln + lnx + ln(-3 + x) = ln(5) + ln(2) 6ln + lnx + (-3 * ln + x * ln) = ln(5) + ln(2) 6ln + lnx + (-3ln + lnx) = ln(5) + ln(2) Reorder the terms: 6ln + -3ln + lnx + lnx = ln(5) + ln(2) Combine like terms: 6ln + -3ln = 3ln 3ln + lnx + lnx = ln(5) + ln(2) Combine like terms: lnx + lnx = 2lnx 3ln + 2lnx = ln(5) + ln(2) Reorder the terms for easier multiplication: 3ln + 2lnx = 5ln + ln(2) Reorder the terms for easier multiplication: 3ln + 2lnx = 5ln + 2ln Combine like terms: 5ln + 2ln = 7ln 3ln + 2lnx = 7ln Solving 3ln + 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. 3ln + -7ln + 2lnx = 7ln + -7ln Combine like terms: 3ln + -7ln = -4ln -4ln + 2lnx = 7ln + -7ln Combine like terms: 7ln + -7ln = 0 -4ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-2 + x) = 0 Ignore the factor 2.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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -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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