ln(x^2-4)=ln(2x+11)

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Solution for ln(x^2-4)=ln(2x+11) equation:


Simplifying
ln(x2 + -4) = ln(2x + 11)

Reorder the terms:
ln(-4 + x2) = ln(2x + 11)
(-4 * ln + x2 * ln) = ln(2x + 11)
(-4ln + lnx2) = ln(2x + 11)

Reorder the terms:
-4ln + lnx2 = ln(11 + 2x)
-4ln + lnx2 = (11 * ln + 2x * ln)
-4ln + lnx2 = (11ln + 2lnx)

Solving
-4ln + lnx2 = 11ln + 2lnx

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 + lnx2 = 11ln + -11ln + 2lnx

Combine like terms: -4ln + -11ln = -15ln
-15ln + lnx2 = 11ln + -11ln + 2lnx

Combine like terms: 11ln + -11ln = 0
-15ln + lnx2 = 0 + 2lnx
-15ln + lnx2 = 2lnx

Add '-2lnx' to each side of the equation.
-15ln + -2lnx + lnx2 = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-15ln + -2lnx + lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-15 + -2x + x2) = 0

Factor a trinomial.
ln((-3 + -1x)(5 + -1x)) = 0

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 '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Add 'x' to each side of the equation. -1x + x = 3 + x Combine like terms: -1x + x = 0 0 = 3 + x Simplifying 0 = 3 + 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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + 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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