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