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