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Simplifying ln(7 + 2x) = ln(1 + 4x) (7 * ln + 2x * ln) = ln(1 + 4x) (7ln + 2lnx) = ln(1 + 4x) 7ln + 2lnx = (1 * ln + 4x * ln) 7ln + 2lnx = (1ln + 4lnx) Solving 7ln + 2lnx = 1ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. 7ln + -1ln + 2lnx = 1ln + -1ln + 4lnx Combine like terms: 7ln + -1ln = 6ln 6ln + 2lnx = 1ln + -1ln + 4lnx Combine like terms: 1ln + -1ln = 0 6ln + 2lnx = 0 + 4lnx 6ln + 2lnx = 4lnx Add '-4lnx' to each side of the equation. 6ln + 2lnx + -4lnx = 4lnx + -4lnx Combine like terms: 2lnx + -4lnx = -2lnx 6ln + -2lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 6ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(3 + -1x) = 0 Ignore the factor 2.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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + x 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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