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Simplifying ln(x + 1) + ln(x) = ln(12) Reorder the terms: ln(1 + x) + ln(x) = ln(12) (1 * ln + x * ln) + ln(x) = ln(12) (1ln + lnx) + ln(x) = ln(12) Multiply ln * x 1ln + lnx + lnx = ln(12) Combine like terms: lnx + lnx = 2lnx 1ln + 2lnx = ln(12) Reorder the terms for easier multiplication: 1ln + 2lnx = 12ln Solving 1ln + 2lnx = 12ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. 1ln + -12ln + 2lnx = 12ln + -12ln Combine like terms: 1ln + -12ln = -11ln -11ln + 2lnx = 12ln + -12ln Combine like terms: 12ln + -12ln = 0 -11ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-11 + 2x) = 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 '(-11 + 2x)' equal to zero and attempt to solve: Simplifying -11 + 2x = 0 Solving -11 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + 2x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 2x = 0 + 11 2x = 0 + 11 Combine like terms: 0 + 11 = 11 2x = 11 Add '-2x' to each side of the equation. 2x + -2x = 11 + -2x Combine like terms: 2x + -2x = 0 0 = 11 + -2x Simplifying 0 = 11 + -2x 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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