ln(x^2-1)-3lnx=ln(2)

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Solution for ln(x^2-1)-3lnx=ln(2) equation: 


Simplifying
ln(x2 + -1) + -3lnx = ln(2)

Reorder the terms:
ln(-1 + x2) + -3lnx = ln(2)
(-1 * ln + x2 * ln) + -3lnx = ln(2)
(-1ln + lnx2) + -3lnx = ln(2)

Reorder the terms:
-1ln + -3lnx + lnx2 = ln(2)

Reorder the terms for easier multiplication:
-1ln + -3lnx + lnx2 = 2ln

Solving
-1ln + -3lnx + lnx2 = 2ln

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '-2ln' to each side of the equation.
-1ln + -3lnx + -2ln + lnx2 = 2ln + -2ln

Reorder the terms:
-1ln + -2ln + -3lnx + lnx2 = 2ln + -2ln

Combine like terms: -1ln + -2ln = -3ln
-3ln + -3lnx + lnx2 = 2ln + -2ln

Combine like terms: 2ln + -2ln = 0
-3ln + -3lnx + lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-3 + -3x + x2) = 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 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
-3 + -3x + x2 = 0

Solving
-3 + -3x + x2 = 0

Move all terms containing l to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + -3x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -3x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -3x + x2 = 0 + 3
-3x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-3x + x2 = 3

Add '3x' to each side of the equation.
-3x + 3x + x2 = 3 + 3x

Combine like terms: -3x + 3x = 0
0 + x2 = 3 + 3x
x2 = 3 + 3x

Add '-1x2' to each side of the equation.
x2 + -1x2 = 3 + 3x + -1x2

Combine like terms: x2 + -1x2 = 0
0 = 3 + 3x + -1x2

Simplifying
0 = 3 + 3x + -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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