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Simplifying -4ln(x + 3) + 8ln(x + 5) = 0 Reorder the terms: -4ln(3 + x) + 8ln(x + 5) = 0 (3 * -4ln + x * -4ln) + 8ln(x + 5) = 0 (-12ln + -4lnx) + 8ln(x + 5) = 0 Reorder the terms: -12ln + -4lnx + 8ln(5 + x) = 0 -12ln + -4lnx + (5 * 8ln + x * 8ln) = 0 -12ln + -4lnx + (40ln + 8lnx) = 0 Reorder the terms: -12ln + 40ln + -4lnx + 8lnx = 0 Combine like terms: -12ln + 40ln = 28ln 28ln + -4lnx + 8lnx = 0 Combine like terms: -4lnx + 8lnx = 4lnx 28ln + 4lnx = 0 Solving 28ln + 4lnx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '4ln'. 4ln(7 + 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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Add '-1x' to each side of the equation. x + -1x = -7 + -1x Combine like terms: x + -1x = 0 0 = -7 + -1x Simplifying 0 = -7 + -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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