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Simplifying ln(x + 6) + -1ln(3) = ln(16) Reorder the terms: ln(6 + x) + -1ln(3) = ln(16) (6 * ln + x * ln) + -1ln(3) = ln(16) (6ln + lnx) + -1ln(3) = ln(16) Reorder the terms for easier multiplication: 6ln + lnx + -1 * 3ln = ln(16) Multiply -1 * 3 6ln + lnx + -3ln = ln(16) Reorder the terms: 6ln + -3ln + lnx = ln(16) Combine like terms: 6ln + -3ln = 3ln 3ln + lnx = ln(16) Reorder the terms for easier multiplication: 3ln + lnx = 16ln Solving 3ln + lnx = 16ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-16ln' to each side of the equation. 3ln + -16ln + lnx = 16ln + -16ln Combine like terms: 3ln + -16ln = -13ln -13ln + lnx = 16ln + -16ln Combine like terms: 16ln + -16ln = 0 -13ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-13 + x) = 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 '(-13 + x)' equal to zero and attempt to solve: Simplifying -13 + x = 0 Solving -13 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + x = 0 + 13 x = 0 + 13 Combine like terms: 0 + 13 = 13 x = 13 Add '-1x' to each side of the equation. x + -1x = 13 + -1x Combine like terms: x + -1x = 0 0 = 13 + -1x Simplifying 0 = 13 + -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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