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Simplifying ln(x + 3) + ln(x + 6) = ln(5) + ln(2) Reorder the terms: ln(3 + x) + ln(x + 6) = ln(5) + ln(2) (3 * ln + x * ln) + ln(x + 6) = ln(5) + ln(2) (3ln + lnx) + ln(x + 6) = ln(5) + ln(2) Reorder the terms: 3ln + lnx + ln(6 + x) = ln(5) + ln(2) 3ln + lnx + (6 * ln + x * ln) = ln(5) + ln(2) 3ln + lnx + (6ln + lnx) = ln(5) + ln(2) Reorder the terms: 3ln + 6ln + lnx + lnx = ln(5) + ln(2) Combine like terms: 3ln + 6ln = 9ln 9ln + lnx + lnx = ln(5) + ln(2) Combine like terms: lnx + lnx = 2lnx 9ln + 2lnx = ln(5) + ln(2) Reorder the terms for easier multiplication: 9ln + 2lnx = 5ln + ln(2) Reorder the terms for easier multiplication: 9ln + 2lnx = 5ln + 2ln Combine like terms: 5ln + 2ln = 7ln 9ln + 2lnx = 7ln Solving 9ln + 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. 9ln + -7ln + 2lnx = 7ln + -7ln Combine like terms: 9ln + -7ln = 2ln 2ln + 2lnx = 7ln + -7ln Combine like terms: 7ln + -7ln = 0 2ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(1 + 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -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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