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Simplifying ln(4x + -1) + ln(x + 2) = 2ln(x) Reorder the terms: ln(-1 + 4x) + ln(x + 2) = 2ln(x) (-1 * ln + 4x * ln) + ln(x + 2) = 2ln(x) (-1ln + 4lnx) + ln(x + 2) = 2ln(x) Reorder the terms: -1ln + 4lnx + ln(2 + x) = 2ln(x) -1ln + 4lnx + (2 * ln + x * ln) = 2ln(x) -1ln + 4lnx + (2ln + lnx) = 2ln(x) Reorder the terms: -1ln + 2ln + 4lnx + lnx = 2ln(x) Combine like terms: -1ln + 2ln = 1ln 1ln + 4lnx + lnx = 2ln(x) Combine like terms: 4lnx + lnx = 5lnx 1ln + 5lnx = 2ln(x) Multiply ln * x 1ln + 5lnx = 2lnx Solving 1ln + 5lnx = 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2lnx' to each side of the equation. 1ln + 5lnx + -2lnx = 2lnx + -2lnx Combine like terms: 5lnx + -2lnx = 3lnx 1ln + 3lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 1ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + 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 '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Add '-3x' to each side of the equation. 3x + -3x = -1 + -3x Combine like terms: 3x + -3x = 0 0 = -1 + -3x Simplifying 0 = -1 + -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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