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Simplifying ln(x + 2) + ln(x) = ln(x + 56) Reorder the terms: ln(2 + x) + ln(x) = ln(x + 56) (2 * ln + x * ln) + ln(x) = ln(x + 56) (2ln + lnx) + ln(x) = ln(x + 56) Multiply ln * x 2ln + lnx + lnx = ln(x + 56) Combine like terms: lnx + lnx = 2lnx 2ln + 2lnx = ln(x + 56) Reorder the terms: 2ln + 2lnx = ln(56 + x) 2ln + 2lnx = (56 * ln + x * ln) 2ln + 2lnx = (56ln + lnx) Solving 2ln + 2lnx = 56ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-56ln' to each side of the equation. 2ln + -56ln + 2lnx = 56ln + -56ln + lnx Combine like terms: 2ln + -56ln = -54ln -54ln + 2lnx = 56ln + -56ln + lnx Combine like terms: 56ln + -56ln = 0 -54ln + 2lnx = 0 + lnx -54ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -54ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -54ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -54ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-54 + x) = 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 '(-54 + x)' equal to zero and attempt to solve: Simplifying -54 + x = 0 Solving -54 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '54' to each side of the equation. -54 + 54 + x = 0 + 54 Combine like terms: -54 + 54 = 0 0 + x = 0 + 54 x = 0 + 54 Combine like terms: 0 + 54 = 54 x = 54 Add '-1x' to each side of the equation. x + -1x = 54 + -1x Combine like terms: x + -1x = 0 0 = 54 + -1x Simplifying 0 = 54 + -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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