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Simplifying ln(x2 + 6) = ln(15) Reorder the terms: ln(6 + x2) = ln(15) (6 * ln + x2 * ln) = ln(15) (6ln + lnx2) = ln(15) Reorder the terms for easier multiplication: 6ln + lnx2 = 15ln Solving 6ln + lnx2 = 15ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-15ln' to each side of the equation. 6ln + -15ln + lnx2 = 15ln + -15ln Combine like terms: 6ln + -15ln = -9ln -9ln + lnx2 = 15ln + -15ln Combine like terms: 15ln + -15ln = 0 -9ln + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-9 + x2) = 0 Factor a difference between two squares. ln((3 + x)(-3 + 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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -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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