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Simplifying ln(7x + -1) + ln(2) = ln(x + -7) Reorder the terms: ln(-1 + 7x) + ln(2) = ln(x + -7) (-1 * ln + 7x * ln) + ln(2) = ln(x + -7) (-1ln + 7lnx) + ln(2) = ln(x + -7) Reorder the terms for easier multiplication: -1ln + 7lnx + 2ln = ln(x + -7) Reorder the terms: -1ln + 2ln + 7lnx = ln(x + -7) Combine like terms: -1ln + 2ln = 1ln 1ln + 7lnx = ln(x + -7) Reorder the terms: 1ln + 7lnx = ln(-7 + x) 1ln + 7lnx = (-7 * ln + x * ln) 1ln + 7lnx = (-7ln + lnx) Solving 1ln + 7lnx = -7ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '7ln' to each side of the equation. 1ln + 7ln + 7lnx = -7ln + 7ln + lnx Combine like terms: 1ln + 7ln = 8ln 8ln + 7lnx = -7ln + 7ln + lnx Combine like terms: -7ln + 7ln = 0 8ln + 7lnx = 0 + lnx 8ln + 7lnx = lnx Add '-1lnx' to each side of the equation. 8ln + 7lnx + -1lnx = lnx + -1lnx Combine like terms: 7lnx + -1lnx = 6lnx 8ln + 6lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 8ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(4 + 3x) = 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 '(4 + 3x)' equal to zero and attempt to solve: Simplifying 4 + 3x = 0 Solving 4 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x = 0 + -4 3x = 0 + -4 Combine like terms: 0 + -4 = -4 3x = -4 Add '-3x' to each side of the equation. 3x + -3x = -4 + -3x Combine like terms: 3x + -3x = 0 0 = -4 + -3x Simplifying 0 = -4 + -3x 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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