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Simplifying ln(x2 + 4x) = ln(x2 + 16) Reorder the terms: ln(4x + x2) = ln(x2 + 16) (4x * ln + x2 * ln) = ln(x2 + 16) (4lnx + lnx2) = ln(x2 + 16) Reorder the terms: 4lnx + lnx2 = ln(16 + x2) 4lnx + lnx2 = (16 * ln + x2 * ln) 4lnx + lnx2 = (16ln + lnx2) Add '-1lnx2' to each side of the equation. 4lnx + lnx2 + -1lnx2 = 16ln + lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 4lnx + 0 = 16ln + lnx2 + -1lnx2 4lnx = 16ln + lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 4lnx = 16ln + 0 4lnx = 16ln Solving 4lnx = 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. -16ln + 4lnx = 16ln + -16ln Combine like terms: 16ln + -16ln = 0 -16ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), '4ln'. 4ln(-4 + x) = 0 Ignore the factor 4.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 '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Add '-1x' to each side of the equation. x + -1x = 4 + -1x Combine like terms: x + -1x = 0 0 = 4 + -1x Simplifying 0 = 4 + -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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