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Simplifying ln(5x + -5) + ln(x + 1) = 2ln(2x) Reorder the terms: ln(-5 + 5x) + ln(x + 1) = 2ln(2x) (-5 * ln + 5x * ln) + ln(x + 1) = 2ln(2x) (-5ln + 5lnx) + ln(x + 1) = 2ln(2x) Reorder the terms: -5ln + 5lnx + ln(1 + x) = 2ln(2x) -5ln + 5lnx + (1 * ln + x * ln) = 2ln(2x) -5ln + 5lnx + (1ln + lnx) = 2ln(2x) Reorder the terms: -5ln + 1ln + 5lnx + lnx = 2ln(2x) Combine like terms: -5ln + 1ln = -4ln -4ln + 5lnx + lnx = 2ln(2x) Combine like terms: 5lnx + lnx = 6lnx -4ln + 6lnx = 2ln(2x) Remove parenthesis around (2x) -4ln + 6lnx = 2ln * 2x Reorder the terms for easier multiplication: -4ln + 6lnx = 2 * 2ln * x Multiply 2 * 2 -4ln + 6lnx = 4ln * x Multiply ln * x -4ln + 6lnx = 4lnx Solving -4ln + 6lnx = 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4lnx' to each side of the equation. -4ln + 6lnx + -4lnx = 4lnx + -4lnx Combine like terms: 6lnx + -4lnx = 2lnx -4ln + 2lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 -4ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-2 + x) = 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 '(-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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