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Simplifying ln(6 + -7x) + -1(2lnx) = ln(3) (6 * ln + -7x * ln) + -1(2lnx) = ln(3) (6ln + -7lnx) + -1(2lnx) = ln(3) Remove parenthesis around (2lnx) 6ln + -7lnx + -1 * 2lnx = ln(3) Multiply -1 * 2 6ln + -7lnx + -2lnx = ln(3) Combine like terms: -7lnx + -2lnx = -9lnx 6ln + -9lnx = ln(3) Reorder the terms for easier multiplication: 6ln + -9lnx = 3ln Solving 6ln + -9lnx = 3ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. 6ln + -3ln + -9lnx = 3ln + -3ln Combine like terms: 6ln + -3ln = 3ln 3ln + -9lnx = 3ln + -3ln Combine like terms: 3ln + -3ln = 0 3ln + -9lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(1 + -3x) = 0 Ignore the factor 3.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 + -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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