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Simplifying ln(6) + ln(x + -1) = ln(3x) Reorder the terms for easier multiplication: 6ln + ln(x + -1) = ln(3x) Reorder the terms: 6ln + ln(-1 + x) = ln(3x) 6ln + (-1 * ln + x * ln) = ln(3x) 6ln + (-1ln + lnx) = ln(3x) Combine like terms: 6ln + -1ln = 5ln 5ln + lnx = ln(3x) Remove parenthesis around (3x) 5ln + lnx = ln * 3x Reorder the terms for easier multiplication: 5ln + lnx = 3ln * x Multiply ln * x 5ln + lnx = 3lnx Solving 5ln + lnx = 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3lnx' to each side of the equation. 5ln + lnx + -3lnx = 3lnx + -3lnx Combine like terms: lnx + -3lnx = -2lnx 5ln + -2lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 5ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(5 + -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 '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Add '2x' to each side of the equation. -2x + 2x = -5 + 2x Combine like terms: -2x + 2x = 0 0 = -5 + 2x Simplifying 0 = -5 + 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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