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Simplifying ln(x) + ln(x + 4) = ln(x + 28) Multiply ln * x lnx + ln(x + 4) = ln(x + 28) Reorder the terms: lnx + ln(4 + x) = ln(x + 28) lnx + (4 * ln + x * ln) = ln(x + 28) lnx + (4ln + lnx) = ln(x + 28) Reorder the terms: 4ln + lnx + lnx = ln(x + 28) Combine like terms: lnx + lnx = 2lnx 4ln + 2lnx = ln(x + 28) Reorder the terms: 4ln + 2lnx = ln(28 + x) 4ln + 2lnx = (28 * ln + x * ln) 4ln + 2lnx = (28ln + lnx) Solving 4ln + 2lnx = 28ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-28ln' to each side of the equation. 4ln + -28ln + 2lnx = 28ln + -28ln + lnx Combine like terms: 4ln + -28ln = -24ln -24ln + 2lnx = 28ln + -28ln + lnx Combine like terms: 28ln + -28ln = 0 -24ln + 2lnx = 0 + lnx -24ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -24ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -24ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -24ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-24 + 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 '(-24 + x)' equal to zero and attempt to solve: Simplifying -24 + x = 0 Solving -24 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = 0 + 24 Combine like terms: -24 + 24 = 0 0 + x = 0 + 24 x = 0 + 24 Combine like terms: 0 + 24 = 24 x = 24 Add '-1x' to each side of the equation. x + -1x = 24 + -1x Combine like terms: x + -1x = 0 0 = 24 + -1x Simplifying 0 = 24 + -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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