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Simplifying ln(x + 5) + -1lnx = ln(3x + -1) Reorder the terms: ln(5 + x) + -1lnx = ln(3x + -1) (5 * ln + x * ln) + -1lnx = ln(3x + -1) (5ln + lnx) + -1lnx = ln(3x + -1) Combine like terms: lnx + -1lnx = 0 5ln + 0 = ln(3x + -1) 5ln = ln(3x + -1) Reorder the terms: 5ln = ln(-1 + 3x) 5ln = (-1 * ln + 3x * ln) 5ln = (-1ln + 3lnx) Solving 5ln = -1ln + 3lnx 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 = -1ln + ln + 3lnx Combine like terms: 5ln + ln = 6ln 6ln = -1ln + ln + 3lnx Combine like terms: -1ln + ln = 0 6ln = 0 + 3lnx 6ln = 3lnx Add '-3lnx' to each side of the equation. 6ln + -3lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 6ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(2 + -1x) = 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 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + 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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