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Simplifying ln(x + 4) + ln(x) = ln(x + 40) Reorder the terms: ln(4 + x) + ln(x) = ln(x + 40) (4 * ln + x * ln) + ln(x) = ln(x + 40) (4ln + lnx) + ln(x) = ln(x + 40) Multiply ln * x 4ln + lnx + lnx = ln(x + 40) Combine like terms: lnx + lnx = 2lnx 4ln + 2lnx = ln(x + 40) Reorder the terms: 4ln + 2lnx = ln(40 + x) 4ln + 2lnx = (40 * ln + x * ln) 4ln + 2lnx = (40ln + lnx) Solving 4ln + 2lnx = 40ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-40ln' to each side of the equation. 4ln + -40ln + 2lnx = 40ln + -40ln + lnx Combine like terms: 4ln + -40ln = -36ln -36ln + 2lnx = 40ln + -40ln + lnx Combine like terms: 40ln + -40ln = 0 -36ln + 2lnx = 0 + lnx -36ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -36ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -36ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -36ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-36 + 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 '(-36 + x)' equal to zero and attempt to solve: Simplifying -36 + x = 0 Solving -36 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = 0 + 36 Combine like terms: -36 + 36 = 0 0 + x = 0 + 36 x = 0 + 36 Combine like terms: 0 + 36 = 36 x = 36 Add '-1x' to each side of the equation. x + -1x = 36 + -1x Combine like terms: x + -1x = 0 0 = 36 + -1x Simplifying 0 = 36 + -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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