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