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Simplifying ln(x + -8) + -1ln(x + 9) = ln(x + -7) Reorder the terms: ln(-8 + x) + -1ln(x + 9) = ln(x + -7) (-8 * ln + x * ln) + -1ln(x + 9) = ln(x + -7) (-8ln + lnx) + -1ln(x + 9) = ln(x + -7) Reorder the terms: -8ln + lnx + -1ln(9 + x) = ln(x + -7) -8ln + lnx + (9 * -1ln + x * -1ln) = ln(x + -7) -8ln + lnx + (-9ln + -1lnx) = ln(x + -7) Reorder the terms: -8ln + -9ln + lnx + -1lnx = ln(x + -7) Combine like terms: -8ln + -9ln = -17ln -17ln + lnx + -1lnx = ln(x + -7) Combine like terms: lnx + -1lnx = 0 -17ln + 0 = ln(x + -7) -17ln = ln(x + -7) Reorder the terms: -17ln = ln(-7 + x) -17ln = (-7 * ln + x * ln) -17ln = (-7ln + lnx) Solving -17ln = -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. -17ln + 7ln = -7ln + 7ln + lnx Combine like terms: -17ln + 7ln = -10ln -10ln = -7ln + 7ln + lnx Combine like terms: -7ln + 7ln = 0 -10ln = 0 + lnx -10ln = lnx Add '-1lnx' to each side of the equation. -10ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -10ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(10 + x) = 0 Ignore the factor -1.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 '(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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