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Simplifying ln(x + -5) + ln(2x + 1) = ln(x2 + 12x + 11) Reorder the terms: ln(-5 + x) + ln(2x + 1) = ln(x2 + 12x + 11) (-5 * ln + x * ln) + ln(2x + 1) = ln(x2 + 12x + 11) (-5ln + lnx) + ln(2x + 1) = ln(x2 + 12x + 11) Reorder the terms: -5ln + lnx + ln(1 + 2x) = ln(x2 + 12x + 11) -5ln + lnx + (1 * ln + 2x * ln) = ln(x2 + 12x + 11) -5ln + lnx + (1ln + 2lnx) = ln(x2 + 12x + 11) Reorder the terms: -5ln + 1ln + lnx + 2lnx = ln(x2 + 12x + 11) Combine like terms: -5ln + 1ln = -4ln -4ln + lnx + 2lnx = ln(x2 + 12x + 11) Combine like terms: lnx + 2lnx = 3lnx -4ln + 3lnx = ln(x2 + 12x + 11) Reorder the terms: -4ln + 3lnx = ln(11 + 12x + x2) -4ln + 3lnx = (11 * ln + 12x * ln + x2 * ln) -4ln + 3lnx = (11ln + 12lnx + lnx2) Solving -4ln + 3lnx = 11ln + 12lnx + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-11ln' to each side of the equation. -4ln + -11ln + 3lnx = 11ln + 12lnx + -11ln + lnx2 Combine like terms: -4ln + -11ln = -15ln -15ln + 3lnx = 11ln + 12lnx + -11ln + lnx2 Reorder the terms: -15ln + 3lnx = 11ln + -11ln + 12lnx + lnx2 Combine like terms: 11ln + -11ln = 0 -15ln + 3lnx = 0 + 12lnx + lnx2 -15ln + 3lnx = 12lnx + lnx2 Add '-12lnx' to each side of the equation. -15ln + 3lnx + -12lnx = 12lnx + -12lnx + lnx2 Combine like terms: 3lnx + -12lnx = -9lnx -15ln + -9lnx = 12lnx + -12lnx + lnx2 Combine like terms: 12lnx + -12lnx = 0 -15ln + -9lnx = 0 + lnx2 -15ln + -9lnx = lnx2 Add '-1lnx2' to each side of the equation. -15ln + -9lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -15ln + -9lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(15 + 9x + x2) = 0 Ignore the factor -1.Subproblem 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 '(15 + 9x + x2)' equal to zero and attempt to solve: Simplifying 15 + 9x + x2 = 0 Solving 15 + 9x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + 9x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 9x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 9x + x2 = 0 + -15 9x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 9x + x2 = -15 Add '-9x' to each side of the equation. 9x + -9x + x2 = -15 + -9x Combine like terms: 9x + -9x = 0 0 + x2 = -15 + -9x x2 = -15 + -9x Add '-1x2' to each side of the equation. x2 + -1x2 = -15 + -9x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -15 + -9x + -1x2 Simplifying 0 = -15 + -9x + -1x2 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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