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