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Simplifying ln(5x + -3) = ln(x + -1) Reorder the terms: ln(-3 + 5x) = ln(x + -1) (-3 * ln + 5x * ln) = ln(x + -1) (-3ln + 5lnx) = ln(x + -1) Reorder the terms: -3ln + 5lnx = ln(-1 + x) -3ln + 5lnx = (-1 * ln + x * ln) -3ln + 5lnx = (-1ln + lnx) Solving -3ln + 5lnx = -1ln + lnx 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. -3ln + ln + 5lnx = -1ln + ln + lnx Combine like terms: -3ln + ln = -2ln -2ln + 5lnx = -1ln + ln + lnx Combine like terms: -1ln + ln = 0 -2ln + 5lnx = 0 + lnx -2ln + 5lnx = lnx Add '-1lnx' to each side of the equation. -2ln + 5lnx + -1lnx = lnx + -1lnx Combine like terms: 5lnx + -1lnx = 4lnx -2ln + 4lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -2ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-1 + 2x) = 0 Ignore the factor 2.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 '(-1 + 2x)' equal to zero and attempt to solve: Simplifying -1 + 2x = 0 Solving -1 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x = 0 + 1 2x = 0 + 1 Combine like terms: 0 + 1 = 1 2x = 1 Add '-2x' to each side of the equation. 2x + -2x = 1 + -2x Combine like terms: 2x + -2x = 0 0 = 1 + -2x Simplifying 0 = 1 + -2x 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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