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Simplifying ln(x + -3) + ln(2x + 3) = ln(-4x2) Reorder the terms: ln(-3 + x) + ln(2x + 3) = ln(-4x2) (-3 * ln + x * ln) + ln(2x + 3) = ln(-4x2) (-3ln + lnx) + ln(2x + 3) = ln(-4x2) Reorder the terms: -3ln + lnx + ln(3 + 2x) = ln(-4x2) -3ln + lnx + (3 * ln + 2x * ln) = ln(-4x2) -3ln + lnx + (3ln + 2lnx) = ln(-4x2) Reorder the terms: -3ln + 3ln + lnx + 2lnx = ln(-4x2) Combine like terms: -3ln + 3ln = 0 0 + lnx + 2lnx = ln(-4x2) lnx + 2lnx = ln(-4x2) Combine like terms: lnx + 2lnx = 3lnx 3lnx = ln(-4x2) Remove parenthesis around (-4x2) 3lnx = ln * -4x2 Reorder the terms for easier multiplication: 3lnx = -4ln * x2 Multiply ln * x2 3lnx = -4lnx2 Solving 3lnx = -4lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '4lnx2' to each side of the equation. 3lnx + 4lnx2 = -4lnx2 + 4lnx2 Combine like terms: -4lnx2 + 4lnx2 = 0 3lnx + 4lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'lnx'. lnx(3 + 4x) = 0Subproblem 1
Set the factor 'lnx' equal to zero and attempt to solve: Simplifying lnx = 0 Solving lnx = 0 Move all terms containing l to the left, all other terms to the right. Simplifying lnx = 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 '(3 + 4x)' equal to zero and attempt to solve: Simplifying 3 + 4x = 0 Solving 3 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Add '-4x' to each side of the equation. 4x + -4x = -3 + -4x Combine like terms: 4x + -4x = 0 0 = -3 + -4x Simplifying 0 = -3 + -4x 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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