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Simplifying ln(x + -6) + ln(x + 3) = ln(22) Reorder the terms: ln(-6 + x) + ln(x + 3) = ln(22) (-6 * ln + x * ln) + ln(x + 3) = ln(22) (-6ln + lnx) + ln(x + 3) = ln(22) Reorder the terms: -6ln + lnx + ln(3 + x) = ln(22) -6ln + lnx + (3 * ln + x * ln) = ln(22) -6ln + lnx + (3ln + lnx) = ln(22) Reorder the terms: -6ln + 3ln + lnx + lnx = ln(22) Combine like terms: -6ln + 3ln = -3ln -3ln + lnx + lnx = ln(22) Combine like terms: lnx + lnx = 2lnx -3ln + 2lnx = ln(22) Reorder the terms for easier multiplication: -3ln + 2lnx = 22ln Solving -3ln + 2lnx = 22ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-22ln' to each side of the equation. -3ln + -22ln + 2lnx = 22ln + -22ln Combine like terms: -3ln + -22ln = -25ln -25ln + 2lnx = 22ln + -22ln Combine like terms: 22ln + -22ln = 0 -25ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-25 + 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 '(-25 + 2x)' equal to zero and attempt to solve: Simplifying -25 + 2x = 0 Solving -25 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + 2x = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 2x = 0 + 25 2x = 0 + 25 Combine like terms: 0 + 25 = 25 2x = 25 Add '-2x' to each side of the equation. 2x + -2x = 25 + -2x Combine like terms: 2x + -2x = 0 0 = 25 + -2x Simplifying 0 = 25 + -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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