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Simplifying ln(x + 3) + -1lnx = 5ln(x2 + -4) Reorder the terms: ln(3 + x) + -1lnx = 5ln(x2 + -4) (3 * ln + x * ln) + -1lnx = 5ln(x2 + -4) (3ln + lnx) + -1lnx = 5ln(x2 + -4) Combine like terms: lnx + -1lnx = 0 3ln + 0 = 5ln(x2 + -4) 3ln = 5ln(x2 + -4) Reorder the terms: 3ln = 5ln(-4 + x2) 3ln = (-4 * 5ln + x2 * 5ln) 3ln = (-20ln + 5lnx2) Solving 3ln = -20ln + 5lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '20ln' to each side of the equation. 3ln + 20ln = -20ln + 20ln + 5lnx2 Combine like terms: 3ln + 20ln = 23ln 23ln = -20ln + 20ln + 5lnx2 Combine like terms: -20ln + 20ln = 0 23ln = 0 + 5lnx2 23ln = 5lnx2 Add '-5lnx2' to each side of the equation. 23ln + -5lnx2 = 5lnx2 + -5lnx2 Combine like terms: 5lnx2 + -5lnx2 = 0 23ln + -5lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(23 + -5x2) = 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 '(23 + -5x2)' equal to zero and attempt to solve: Simplifying 23 + -5x2 = 0 Solving 23 + -5x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + -5x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -5x2 = 0 + -23 -5x2 = 0 + -23 Combine like terms: 0 + -23 = -23 -5x2 = -23 Add '5x2' to each side of the equation. -5x2 + 5x2 = -23 + 5x2 Combine like terms: -5x2 + 5x2 = 0 0 = -23 + 5x2 Simplifying 0 = -23 + 5x2 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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