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Simplifying ln(8x + 5) = ln(5x + -1) Reorder the terms: ln(5 + 8x) = ln(5x + -1) (5 * ln + 8x * ln) = ln(5x + -1) (5ln + 8lnx) = ln(5x + -1) Reorder the terms: 5ln + 8lnx = ln(-1 + 5x) 5ln + 8lnx = (-1 * ln + 5x * ln) 5ln + 8lnx = (-1ln + 5lnx) Solving 5ln + 8lnx = -1ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'ln' to each side of the equation. 5ln + ln + 8lnx = -1ln + ln + 5lnx Combine like terms: 5ln + ln = 6ln 6ln + 8lnx = -1ln + ln + 5lnx Combine like terms: -1ln + ln = 0 6ln + 8lnx = 0 + 5lnx 6ln + 8lnx = 5lnx Add '-5lnx' to each side of the equation. 6ln + 8lnx + -5lnx = 5lnx + -5lnx Combine like terms: 8lnx + -5lnx = 3lnx 6ln + 3lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 6ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(2 + x) = 0 Ignore the factor 3.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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -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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