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Simplifying ln(2x + 7) = ln(t + 1) + ln(3) Reorder the terms: ln(7 + 2x) = ln(t + 1) + ln(3) (7 * ln + 2x * ln) = ln(t + 1) + ln(3) (7ln + 2lnx) = ln(t + 1) + ln(3) Reorder the terms: 7ln + 2lnx = ln(1 + t) + ln(3) 7ln + 2lnx = (1 * ln + t * ln) + ln(3) 7ln + 2lnx = (1ln + lnt) + ln(3) Reorder the terms for easier multiplication: 7ln + 2lnx = 1ln + lnt + 3ln Reorder the terms: 7ln + 2lnx = 1ln + 3ln + lnt Combine like terms: 1ln + 3ln = 4ln 7ln + 2lnx = 4ln + lnt Solving 7ln + 2lnx = 4ln + lnt Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. 7ln + -4ln + 2lnx = 4ln + -4ln + lnt Combine like terms: 7ln + -4ln = 3ln 3ln + 2lnx = 4ln + -4ln + lnt Combine like terms: 4ln + -4ln = 0 3ln + 2lnx = 0 + lnt 3ln + 2lnx = lnt Add '-1lnt' to each side of the equation. 3ln + -1lnt + 2lnx = lnt + -1lnt Combine like terms: lnt + -1lnt = 0 3ln + -1lnt + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(3 + -1t + 2x) = 0Subproblem 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 '(3 + -1t + 2x)' equal to zero and attempt to solve: Simplifying 3 + -1t + 2x = 0 Solving 3 + -1t + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -1t + -3 + 2x = 0 + -3 Reorder the terms: 3 + -3 + -1t + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t + 2x = 0 + -3 -1t + 2x = 0 + -3 Combine like terms: 0 + -3 = -3 -1t + 2x = -3 Add 't' to each side of the equation. -1t + t + 2x = -3 + t Combine like terms: -1t + t = 0 0 + 2x = -3 + t 2x = -3 + t Add '-2x' to each side of the equation. 2x + -2x = -3 + t + -2x Combine like terms: 2x + -2x = 0 0 = -3 + t + -2x Simplifying 0 = -3 + t + -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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