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Simplifying ln(6x + -4) + ln(6x) = 2ln(x) Reorder the terms: ln(-4 + 6x) + ln(6x) = 2ln(x) (-4 * ln + 6x * ln) + ln(6x) = 2ln(x) (-4ln + 6lnx) + ln(6x) = 2ln(x) Remove parenthesis around (6x) -4ln + 6lnx + ln * 6x = 2ln(x) Reorder the terms for easier multiplication: -4ln + 6lnx + 6ln * x = 2ln(x) Multiply ln * x -4ln + 6lnx + 6lnx = 2ln(x) Combine like terms: 6lnx + 6lnx = 12lnx -4ln + 12lnx = 2ln(x) Multiply ln * x -4ln + 12lnx = 2lnx Solving -4ln + 12lnx = 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2lnx' to each side of the equation. -4ln + 12lnx + -2lnx = 2lnx + -2lnx Combine like terms: 12lnx + -2lnx = 10lnx -4ln + 10lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -4ln + 10lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-2 + 5x) = 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 + 5x)' equal to zero and attempt to solve: Simplifying -2 + 5x = 0 Solving -2 + 5x = 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 + 5x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 5x = 0 + 2 5x = 0 + 2 Combine like terms: 0 + 2 = 2 5x = 2 Add '-5x' to each side of the equation. 5x + -5x = 2 + -5x Combine like terms: 5x + -5x = 0 0 = 2 + -5x Simplifying 0 = 2 + -5x 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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