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Simplifying ln(7x + 6) = ln(2x + 1) Reorder the terms: ln(6 + 7x) = ln(2x + 1) (6 * ln + 7x * ln) = ln(2x + 1) (6ln + 7lnx) = ln(2x + 1) Reorder the terms: 6ln + 7lnx = ln(1 + 2x) 6ln + 7lnx = (1 * ln + 2x * ln) 6ln + 7lnx = (1ln + 2lnx) Solving 6ln + 7lnx = 1ln + 2lnx 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. 6ln + -1ln + 7lnx = 1ln + -1ln + 2lnx Combine like terms: 6ln + -1ln = 5ln 5ln + 7lnx = 1ln + -1ln + 2lnx Combine like terms: 1ln + -1ln = 0 5ln + 7lnx = 0 + 2lnx 5ln + 7lnx = 2lnx Add '-2lnx' to each side of the equation. 5ln + 7lnx + -2lnx = 2lnx + -2lnx Combine like terms: 7lnx + -2lnx = 5lnx 5ln + 5lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 5ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), '5ln'. 5ln(1 + x) = 0 Ignore the factor 5.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 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -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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