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Simplifying ln(x + 7) + -1ln(3) = ln(7x + 1) Reorder the terms: ln(7 + x) + -1ln(3) = ln(7x + 1) (7 * ln + x * ln) + -1ln(3) = ln(7x + 1) (7ln + lnx) + -1ln(3) = ln(7x + 1) Reorder the terms for easier multiplication: 7ln + lnx + -1 * 3ln = ln(7x + 1) Multiply -1 * 3 7ln + lnx + -3ln = ln(7x + 1) Reorder the terms: 7ln + -3ln + lnx = ln(7x + 1) Combine like terms: 7ln + -3ln = 4ln 4ln + lnx = ln(7x + 1) Reorder the terms: 4ln + lnx = ln(1 + 7x) 4ln + lnx = (1 * ln + 7x * ln) 4ln + lnx = (1ln + 7lnx) Solving 4ln + lnx = 1ln + 7lnx 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. 4ln + -1ln + lnx = 1ln + -1ln + 7lnx Combine like terms: 4ln + -1ln = 3ln 3ln + lnx = 1ln + -1ln + 7lnx Combine like terms: 1ln + -1ln = 0 3ln + lnx = 0 + 7lnx 3ln + lnx = 7lnx Add '-7lnx' to each side of the equation. 3ln + lnx + -7lnx = 7lnx + -7lnx Combine like terms: lnx + -7lnx = -6lnx 3ln + -6lnx = 7lnx + -7lnx Combine like terms: 7lnx + -7lnx = 0 3ln + -6lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(1 + -2x) = 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 '(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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