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Simplifying ln(2x + -6) + ln(x) = ln(36) Reorder the terms: ln(-6 + 2x) + ln(x) = ln(36) (-6 * ln + 2x * ln) + ln(x) = ln(36) (-6ln + 2lnx) + ln(x) = ln(36) Multiply ln * x -6ln + 2lnx + lnx = ln(36) Combine like terms: 2lnx + lnx = 3lnx -6ln + 3lnx = ln(36) Reorder the terms for easier multiplication: -6ln + 3lnx = 36ln Solving -6ln + 3lnx = 36ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-36ln' to each side of the equation. -6ln + -36ln + 3lnx = 36ln + -36ln Combine like terms: -6ln + -36ln = -42ln -42ln + 3lnx = 36ln + -36ln Combine like terms: 36ln + -36ln = 0 -42ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-14 + x) = 0 Ignore the factor 3.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 '(-14 + x)' equal to zero and attempt to solve: Simplifying -14 + x = 0 Solving -14 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 0 + 14 Combine like terms: -14 + 14 = 0 0 + x = 0 + 14 x = 0 + 14 Combine like terms: 0 + 14 = 14 x = 14 Add '-1x' to each side of the equation. x + -1x = 14 + -1x Combine like terms: x + -1x = 0 0 = 14 + -1x Simplifying 0 = 14 + -1x 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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