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Simplifying ln(x + 4) + ln(x + -4) = ln(8x + 4) Reorder the terms: ln(4 + x) + ln(x + -4) = ln(8x + 4) (4 * ln + x * ln) + ln(x + -4) = ln(8x + 4) (4ln + lnx) + ln(x + -4) = ln(8x + 4) Reorder the terms: 4ln + lnx + ln(-4 + x) = ln(8x + 4) 4ln + lnx + (-4 * ln + x * ln) = ln(8x + 4) 4ln + lnx + (-4ln + lnx) = ln(8x + 4) Reorder the terms: 4ln + -4ln + lnx + lnx = ln(8x + 4) Combine like terms: 4ln + -4ln = 0 0 + lnx + lnx = ln(8x + 4) lnx + lnx = ln(8x + 4) Combine like terms: lnx + lnx = 2lnx 2lnx = ln(8x + 4) Reorder the terms: 2lnx = ln(4 + 8x) 2lnx = (4 * ln + 8x * ln) 2lnx = (4ln + 8lnx) Solving 2lnx = 4ln + 8lnx 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. -4ln + 2lnx = 4ln + -4ln + 8lnx Combine like terms: 4ln + -4ln = 0 -4ln + 2lnx = 0 + 8lnx -4ln + 2lnx = 8lnx Add '-8lnx' to each side of the equation. -4ln + 2lnx + -8lnx = 8lnx + -8lnx Combine like terms: 2lnx + -8lnx = -6lnx -4ln + -6lnx = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 -4ln + -6lnx = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(2 + 3x) = 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 '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Add '-3x' to each side of the equation. 3x + -3x = -2 + -3x Combine like terms: 3x + -3x = 0 0 = -2 + -3x Simplifying 0 = -2 + -3x 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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