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Simplifying ln(x + 8) = ln(x) + ln(x + 3) Reorder the terms: ln(8 + x) = ln(x) + ln(x + 3) (8 * ln + x * ln) = ln(x) + ln(x + 3) (8ln + lnx) = ln(x) + ln(x + 3) Multiply ln * x 8ln + lnx = lnx + ln(x + 3) Reorder the terms: 8ln + lnx = lnx + ln(3 + x) 8ln + lnx = lnx + (3 * ln + x * ln) 8ln + lnx = lnx + (3ln + lnx) Reorder the terms: 8ln + lnx = 3ln + lnx + lnx Combine like terms: lnx + lnx = 2lnx 8ln + lnx = 3ln + 2lnx Solving 8ln + lnx = 3ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. 8ln + -3ln + lnx = 3ln + -3ln + 2lnx Combine like terms: 8ln + -3ln = 5ln 5ln + lnx = 3ln + -3ln + 2lnx Combine like terms: 3ln + -3ln = 0 5ln + lnx = 0 + 2lnx 5ln + lnx = 2lnx Add '-2lnx' to each side of the equation. 5ln + lnx + -2lnx = 2lnx + -2lnx Combine like terms: lnx + -2lnx = -1lnx 5ln + -1lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 5ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(5 + -1x) = 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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + x 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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