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