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Simplifying ln(x + 7) + ln(x + 5) = ln(3) Reorder the terms: ln(7 + x) + ln(x + 5) = ln(3) (7 * ln + x * ln) + ln(x + 5) = ln(3) (7ln + lnx) + ln(x + 5) = ln(3) Reorder the terms: 7ln + lnx + ln(5 + x) = ln(3) 7ln + lnx + (5 * ln + x * ln) = ln(3) 7ln + lnx + (5ln + lnx) = ln(3) Reorder the terms: 7ln + 5ln + lnx + lnx = ln(3) Combine like terms: 7ln + 5ln = 12ln 12ln + lnx + lnx = ln(3) Combine like terms: lnx + lnx = 2lnx 12ln + 2lnx = ln(3) Reorder the terms for easier multiplication: 12ln + 2lnx = 3ln Solving 12ln + 2lnx = 3ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. 12ln + -3ln + 2lnx = 3ln + -3ln Combine like terms: 12ln + -3ln = 9ln 9ln + 2lnx = 3ln + -3ln Combine like terms: 3ln + -3ln = 0 9ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(9 + 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 '(9 + 2x)' equal to zero and attempt to solve: Simplifying 9 + 2x = 0 Solving 9 + 2x = 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 + 2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2x = 0 + -9 2x = 0 + -9 Combine like terms: 0 + -9 = -9 2x = -9 Add '-2x' to each side of the equation. 2x + -2x = -9 + -2x Combine like terms: 2x + -2x = 0 0 = -9 + -2x Simplifying 0 = -9 + -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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