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Simplifying ln(x + 5) = ln(3x + -3) Reorder the terms: ln(5 + x) = ln(3x + -3) (5 * ln + x * ln) = ln(3x + -3) (5ln + lnx) = ln(3x + -3) Reorder the terms: 5ln + lnx = ln(-3 + 3x) 5ln + lnx = (-3 * ln + 3x * ln) 5ln + lnx = (-3ln + 3lnx) Solving 5ln + lnx = -3ln + 3lnx 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. 5ln + 3ln + lnx = -3ln + 3ln + 3lnx Combine like terms: 5ln + 3ln = 8ln 8ln + lnx = -3ln + 3ln + 3lnx Combine like terms: -3ln + 3ln = 0 8ln + lnx = 0 + 3lnx 8ln + lnx = 3lnx Add '-3lnx' to each side of the equation. 8ln + lnx + -3lnx = 3lnx + -3lnx Combine like terms: lnx + -3lnx = -2lnx 8ln + -2lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 8ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(4 + -1x) = 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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + 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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