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Simplifying ln(x + 16) + ln(x) = 3ln(2) Reorder the terms: ln(16 + x) + ln(x) = 3ln(2) (16 * ln + x * ln) + ln(x) = 3ln(2) (16ln + lnx) + ln(x) = 3ln(2) Multiply ln * x 16ln + lnx + lnx = 3ln(2) Combine like terms: lnx + lnx = 2lnx 16ln + 2lnx = 3ln(2) Reorder the terms for easier multiplication: 16ln + 2lnx = 3 * 2ln Multiply 3 * 2 16ln + 2lnx = 6ln Solving 16ln + 2lnx = 6ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. 16ln + -6ln + 2lnx = 6ln + -6ln Combine like terms: 16ln + -6ln = 10ln 10ln + 2lnx = 6ln + -6ln Combine like terms: 6ln + -6ln = 0 10ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(5 + 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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -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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