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Simplifying ln(x + 2) + ln(x) = ln(x + 30) Reorder the terms: ln(2 + x) + ln(x) = ln(x + 30) (2 * ln + x * ln) + ln(x) = ln(x + 30) (2ln + lnx) + ln(x) = ln(x + 30) Multiply ln * x 2ln + lnx + lnx = ln(x + 30) Combine like terms: lnx + lnx = 2lnx 2ln + 2lnx = ln(x + 30) Reorder the terms: 2ln + 2lnx = ln(30 + x) 2ln + 2lnx = (30 * ln + x * ln) 2ln + 2lnx = (30ln + lnx) Solving 2ln + 2lnx = 30ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-30ln' to each side of the equation. 2ln + -30ln + 2lnx = 30ln + -30ln + lnx Combine like terms: 2ln + -30ln = -28ln -28ln + 2lnx = 30ln + -30ln + lnx Combine like terms: 30ln + -30ln = 0 -28ln + 2lnx = 0 + lnx -28ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -28ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -28ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -28ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-28 + 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 '(-28 + x)' equal to zero and attempt to solve: Simplifying -28 + x = 0 Solving -28 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + x = 0 + 28 Combine like terms: -28 + 28 = 0 0 + x = 0 + 28 x = 0 + 28 Combine like terms: 0 + 28 = 28 x = 28 Add '-1x' to each side of the equation. x + -1x = 28 + -1x Combine like terms: x + -1x = 0 0 = 28 + -1x Simplifying 0 = 28 + -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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