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