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Simplifying ln(x2 + -21) = ln(7x + -3) Reorder the terms: ln(-21 + x2) = ln(7x + -3) (-21 * ln + x2 * ln) = ln(7x + -3) (-21ln + lnx2) = ln(7x + -3) Reorder the terms: -21ln + lnx2 = ln(-3 + 7x) -21ln + lnx2 = (-3 * ln + 7x * ln) -21ln + lnx2 = (-3ln + 7lnx) Solving -21ln + lnx2 = -3ln + 7lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '3ln' to each side of the equation. -21ln + 3ln + lnx2 = -3ln + 3ln + 7lnx Combine like terms: -21ln + 3ln = -18ln -18ln + lnx2 = -3ln + 3ln + 7lnx Combine like terms: -3ln + 3ln = 0 -18ln + lnx2 = 0 + 7lnx -18ln + lnx2 = 7lnx Add '-7lnx' to each side of the equation. -18ln + -7lnx + lnx2 = 7lnx + -7lnx Combine like terms: 7lnx + -7lnx = 0 -18ln + -7lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-18 + -7x + x2) = 0 Factor a trinomial. ln((-2 + -1x)(9 + -1x)) = 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 '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Add 'x' to each side of the equation. -1x + x = 2 + x Combine like terms: -1x + x = 0 0 = 2 + x Simplifying 0 = 2 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Add 'x' to each side of the equation. -1x + x = -9 + x Combine like terms: -1x + x = 0 0 = -9 + x Simplifying 0 = -9 + x 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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