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Simplifying ln(x + 1) + ln(8 + -1x) = ln(44 + -5x) Reorder the terms: ln(1 + x) + ln(8 + -1x) = ln(44 + -5x) (1 * ln + x * ln) + ln(8 + -1x) = ln(44 + -5x) (1ln + lnx) + ln(8 + -1x) = ln(44 + -5x) 1ln + lnx + (8 * ln + -1x * ln) = ln(44 + -5x) 1ln + lnx + (8ln + -1lnx) = ln(44 + -5x) Reorder the terms: 1ln + 8ln + lnx + -1lnx = ln(44 + -5x) Combine like terms: 1ln + 8ln = 9ln 9ln + lnx + -1lnx = ln(44 + -5x) Combine like terms: lnx + -1lnx = 0 9ln + 0 = ln(44 + -5x) 9ln = ln(44 + -5x) 9ln = (44 * ln + -5x * ln) 9ln = (44ln + -5lnx) Solving 9ln = 44ln + -5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-44ln' to each side of the equation. 9ln + -44ln = 44ln + -44ln + -5lnx Combine like terms: 9ln + -44ln = -35ln -35ln = 44ln + -44ln + -5lnx Combine like terms: 44ln + -44ln = 0 -35ln = 0 + -5lnx -35ln = -5lnx Add '5lnx' to each side of the equation. -35ln + 5lnx = -5lnx + 5lnx Combine like terms: -5lnx + 5lnx = 0 -35ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), '5ln'. 5ln(-7 + x) = 0 Ignore the factor 5.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 '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Add '-1x' to each side of the equation. x + -1x = 7 + -1x Combine like terms: x + -1x = 0 0 = 7 + -1x Simplifying 0 = 7 + -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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