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Simplifying ln(x + 10) = ln(x + -6) + ln(X + -1) Reorder the terms: ln(10 + x) = ln(x + -6) + ln(X + -1) (10 * ln + x * ln) = ln(x + -6) + ln(X + -1) (10ln + lnx) = ln(x + -6) + ln(X + -1) Reorder the terms: 10ln + lnx = ln(-6 + x) + ln(X + -1) 10ln + lnx = (-6 * ln + x * ln) + ln(X + -1) 10ln + lnx = (-6ln + lnx) + ln(X + -1) Reorder the terms: 10ln + lnx = -6ln + lnx + ln(-1 + X) 10ln + lnx = -6ln + lnx + (-1 * ln + X * ln) 10ln + lnx = -6ln + lnx + (-1ln + lnX) Reorder the terms: 10ln + lnx = -6ln + -1ln + lnX + lnx Combine like terms: -6ln + -1ln = -7ln 10ln + lnx = -7ln + lnX + lnx Add '-1lnx' to each side of the equation. 10ln + lnx + -1lnx = -7ln + lnX + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 10ln + 0 = -7ln + lnX + lnx + -1lnx 10ln = -7ln + lnX + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 10ln = -7ln + lnX + 0 10ln = -7ln + lnX Solving 10ln = -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. 10ln + 7ln = -7ln + 7ln + lnX Combine like terms: 10ln + 7ln = 17ln 17ln = -7ln + 7ln + lnX Combine like terms: -7ln + 7ln = 0 17ln = 0 + lnX 17ln = lnX Add '-1lnX' to each side of the equation. 17ln + -1lnX = lnX + -1lnX Combine like terms: lnX + -1lnX = 0 17ln + -1lnX = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(17 + -1X) = 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 '(17 + -1X)' equal to zero and attempt to solve: Simplifying 17 + -1X = 0 Solving 17 + -1X = 0 Move all terms containing l to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -1X = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -1X = 0 + -17 -1X = 0 + -17 Combine like terms: 0 + -17 = -17 -1X = -17 Add 'X' to each side of the equation. -1X + X = -17 + X Combine like terms: -1X + X = 0 0 = -17 + X Simplifying 0 = -17 + X 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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