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Simplifying ln(2x) + ln(x + -6) = ln(14) Remove parenthesis around (2x) ln * 2x + ln(x + -6) = ln(14) Reorder the terms for easier multiplication: 2ln * x + ln(x + -6) = ln(14) Multiply ln * x 2lnx + ln(x + -6) = ln(14) Reorder the terms: 2lnx + ln(-6 + x) = ln(14) 2lnx + (-6 * ln + x * ln) = ln(14) 2lnx + (-6ln + lnx) = ln(14) Reorder the terms: -6ln + 2lnx + lnx = ln(14) Combine like terms: 2lnx + lnx = 3lnx -6ln + 3lnx = ln(14) Reorder the terms for easier multiplication: -6ln + 3lnx = 14ln Solving -6ln + 3lnx = 14ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-14ln' to each side of the equation. -6ln + -14ln + 3lnx = 14ln + -14ln Combine like terms: -6ln + -14ln = -20ln -20ln + 3lnx = 14ln + -14ln Combine like terms: 14ln + -14ln = 0 -20ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-20 + 3x) = 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 '(-20 + 3x)' equal to zero and attempt to solve: Simplifying -20 + 3x = 0 Solving -20 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + 3x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 3x = 0 + 20 3x = 0 + 20 Combine like terms: 0 + 20 = 20 3x = 20 Add '-3x' to each side of the equation. 3x + -3x = 20 + -3x Combine like terms: 3x + -3x = 0 0 = 20 + -3x Simplifying 0 = 20 + -3x 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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