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