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Simplifying ln(x3 + 9x2 + 27x + 27) = ln(x + 3) + ln(x + 5) Reorder the terms: ln(27 + 27x + 9x2 + x3) = ln(x + 3) + ln(x + 5) (27 * ln + 27x * ln + 9x2 * ln + x3 * ln) = ln(x + 3) + ln(x + 5) (27ln + 27lnx + 9lnx2 + lnx3) = ln(x + 3) + ln(x + 5) Reorder the terms: 27ln + 27lnx + 9lnx2 + lnx3 = ln(3 + x) + ln(x + 5) 27ln + 27lnx + 9lnx2 + lnx3 = (3 * ln + x * ln) + ln(x + 5) 27ln + 27lnx + 9lnx2 + lnx3 = (3ln + lnx) + ln(x + 5) Reorder the terms: 27ln + 27lnx + 9lnx2 + lnx3 = 3ln + lnx + ln(5 + x) 27ln + 27lnx + 9lnx2 + lnx3 = 3ln + lnx + (5 * ln + x * ln) 27ln + 27lnx + 9lnx2 + lnx3 = 3ln + lnx + (5ln + lnx) Reorder the terms: 27ln + 27lnx + 9lnx2 + lnx3 = 3ln + 5ln + lnx + lnx Combine like terms: 3ln + 5ln = 8ln 27ln + 27lnx + 9lnx2 + lnx3 = 8ln + lnx + lnx Combine like terms: lnx + lnx = 2lnx 27ln + 27lnx + 9lnx2 + lnx3 = 8ln + 2lnx Solving 27ln + 27lnx + 9lnx2 + lnx3 = 8ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. 27ln + 27lnx + 9lnx2 + -8ln + lnx3 = 8ln + -8ln + 2lnx Reorder the terms: 27ln + -8ln + 27lnx + 9lnx2 + lnx3 = 8ln + -8ln + 2lnx Combine like terms: 27ln + -8ln = 19ln 19ln + 27lnx + 9lnx2 + lnx3 = 8ln + -8ln + 2lnx Combine like terms: 8ln + -8ln = 0 19ln + 27lnx + 9lnx2 + lnx3 = 0 + 2lnx 19ln + 27lnx + 9lnx2 + lnx3 = 2lnx Add '-2lnx' to each side of the equation. 19ln + 27lnx + 9lnx2 + -2lnx + lnx3 = 2lnx + -2lnx Reorder the terms: 19ln + 27lnx + -2lnx + 9lnx2 + lnx3 = 2lnx + -2lnx Combine like terms: 27lnx + -2lnx = 25lnx 19ln + 25lnx + 9lnx2 + lnx3 = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 19ln + 25lnx + 9lnx2 + lnx3 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(19 + 25x + 9x2 + x3) = 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 '(19 + 25x + 9x2 + x3)' equal to zero and attempt to solve: Simplifying 19 + 25x + 9x2 + x3 = 0 Solving 19 + 25x + 9x2 + x3 = 0 Move all terms containing l to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + 25x + 9x2 + -19 + x3 = 0 + -19 Reorder the terms: 19 + -19 + 25x + 9x2 + x3 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 25x + 9x2 + x3 = 0 + -19 25x + 9x2 + x3 = 0 + -19 Combine like terms: 0 + -19 = -19 25x + 9x2 + x3 = -19 Add '-25x' to each side of the equation. 25x + 9x2 + -25x + x3 = -19 + -25x Reorder the terms: 25x + -25x + 9x2 + x3 = -19 + -25x Combine like terms: 25x + -25x = 0 0 + 9x2 + x3 = -19 + -25x 9x2 + x3 = -19 + -25x Add '-9x2' to each side of the equation. 9x2 + -9x2 + x3 = -19 + -25x + -9x2 Combine like terms: 9x2 + -9x2 = 0 0 + x3 = -19 + -25x + -9x2 x3 = -19 + -25x + -9x2 Add '-1x3' to each side of the equation. x3 + -1x3 = -19 + -25x + -9x2 + -1x3 Combine like terms: x3 + -1x3 = 0 0 = -19 + -25x + -9x2 + -1x3 Simplifying 0 = -19 + -25x + -9x2 + -1x3 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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