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