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Simplifying ln(2x + -2) + ln(4x + -3) = 2ln(2x) Reorder the terms: ln(-2 + 2x) + ln(4x + -3) = 2ln(2x) (-2 * ln + 2x * ln) + ln(4x + -3) = 2ln(2x) (-2ln + 2lnx) + ln(4x + -3) = 2ln(2x) Reorder the terms: -2ln + 2lnx + ln(-3 + 4x) = 2ln(2x) -2ln + 2lnx + (-3 * ln + 4x * ln) = 2ln(2x) -2ln + 2lnx + (-3ln + 4lnx) = 2ln(2x) Reorder the terms: -2ln + -3ln + 2lnx + 4lnx = 2ln(2x) Combine like terms: -2ln + -3ln = -5ln -5ln + 2lnx + 4lnx = 2ln(2x) Combine like terms: 2lnx + 4lnx = 6lnx -5ln + 6lnx = 2ln(2x) Remove parenthesis around (2x) -5ln + 6lnx = 2ln * 2x Reorder the terms for easier multiplication: -5ln + 6lnx = 2 * 2ln * x Multiply 2 * 2 -5ln + 6lnx = 4ln * x Multiply ln * x -5ln + 6lnx = 4lnx Solving -5ln + 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. -5ln + 6lnx + -4lnx = 4lnx + -4lnx Combine like terms: 6lnx + -4lnx = 2lnx -5ln + 2lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 -5ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-5 + 2x) = 0Subproblem 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 '(-5 + 2x)' equal to zero and attempt to solve: Simplifying -5 + 2x = 0 Solving -5 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x = 0 + 5 2x = 0 + 5 Combine like terms: 0 + 5 = 5 2x = 5 Add '-2x' to each side of the equation. 2x + -2x = 5 + -2x Combine like terms: 2x + -2x = 0 0 = 5 + -2x Simplifying 0 = 5 + -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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