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Simplifying ln(4x + -6) + ln(6x) = 2ln(x) Reorder the terms: ln(-6 + 4x) + ln(6x) = 2ln(x) (-6 * ln + 4x * ln) + ln(6x) = 2ln(x) (-6ln + 4lnx) + ln(6x) = 2ln(x) Remove parenthesis around (6x) -6ln + 4lnx + ln * 6x = 2ln(x) Reorder the terms for easier multiplication: -6ln + 4lnx + 6ln * x = 2ln(x) Multiply ln * x -6ln + 4lnx + 6lnx = 2ln(x) Combine like terms: 4lnx + 6lnx = 10lnx -6ln + 10lnx = 2ln(x) Multiply ln * x -6ln + 10lnx = 2lnx Solving -6ln + 10lnx = 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. -6ln + 10lnx + -2lnx = 2lnx + -2lnx Combine like terms: 10lnx + -2lnx = 8lnx -6ln + 8lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -6ln + 8lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-3 + 4x) = 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 '(-3 + 4x)' equal to zero and attempt to solve: Simplifying -3 + 4x = 0 Solving -3 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4x = 0 + 3 4x = 0 + 3 Combine like terms: 0 + 3 = 3 4x = 3 Add '-4x' to each side of the equation. 4x + -4x = 3 + -4x Combine like terms: 4x + -4x = 0 0 = 3 + -4x Simplifying 0 = 3 + -4x 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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