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Simplifying ln(x + -6) + ln(x + 1) = ln(x + -15) Reorder the terms: ln(-6 + x) + ln(x + 1) = ln(x + -15) (-6 * ln + x * ln) + ln(x + 1) = ln(x + -15) (-6ln + lnx) + ln(x + 1) = ln(x + -15) Reorder the terms: -6ln + lnx + ln(1 + x) = ln(x + -15) -6ln + lnx + (1 * ln + x * ln) = ln(x + -15) -6ln + lnx + (1ln + lnx) = ln(x + -15) Reorder the terms: -6ln + 1ln + lnx + lnx = ln(x + -15) Combine like terms: -6ln + 1ln = -5ln -5ln + lnx + lnx = ln(x + -15) Combine like terms: lnx + lnx = 2lnx -5ln + 2lnx = ln(x + -15) Reorder the terms: -5ln + 2lnx = ln(-15 + x) -5ln + 2lnx = (-15 * ln + x * ln) -5ln + 2lnx = (-15ln + lnx) Solving -5ln + 2lnx = -15ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '15ln' to each side of the equation. -5ln + 15ln + 2lnx = -15ln + 15ln + lnx Combine like terms: -5ln + 15ln = 10ln 10ln + 2lnx = -15ln + 15ln + lnx Combine like terms: -15ln + 15ln = 0 10ln + 2lnx = 0 + lnx 10ln + 2lnx = lnx Add '-1lnx' to each side of the equation. 10ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx 10ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 10ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(10 + x) = 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 '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Add '-1x' to each side of the equation. x + -1x = -10 + -1x Combine like terms: x + -1x = 0 0 = -10 + -1x Simplifying 0 = -10 + -1x 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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