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Simplifying 0 = ln(7x + 6) Reorder the terms: 0 = ln(6 + 7x) 0 = (6 * ln + 7x * ln) 0 = (6ln + 7lnx) Solving 0 = 6ln + 7lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. 0 + -6ln = 6ln + -6ln + 7lnx Remove the zero: -6ln = 6ln + -6ln + 7lnx Combine like terms: 6ln + -6ln = 0 -6ln = 0 + 7lnx -6ln = 7lnx Add '-7lnx' to each side of the equation. -6ln + -7lnx = 7lnx + -7lnx Combine like terms: 7lnx + -7lnx = 0 -6ln + -7lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(6 + 7x) = 0 Ignore the factor -1.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 '(6 + 7x)' equal to zero and attempt to solve: Simplifying 6 + 7x = 0 Solving 6 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 7x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 7x = 0 + -6 7x = 0 + -6 Combine like terms: 0 + -6 = -6 7x = -6 Add '-7x' to each side of the equation. 7x + -7x = -6 + -7x Combine like terms: 7x + -7x = 0 0 = -6 + -7x Simplifying 0 = -6 + -7x 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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