ln(7)+ln(2-4x^2)=ln(14)

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Solution for ln(7)+ln(2-4x^2)=ln(14) equation: 


Simplifying
ln(7) + ln(2 + -4x2) = ln(14)

Reorder the terms for easier multiplication:
7ln + ln(2 + -4x2) = ln(14)
7ln + (2 * ln + -4x2 * ln) = ln(14)
7ln + (2ln + -4lnx2) = ln(14)

Combine like terms: 7ln + 2ln = 9ln
9ln + -4lnx2 = ln(14)

Reorder the terms for easier multiplication:
9ln + -4lnx2 = 14ln

Solving
9ln + -4lnx2 = 14ln

Solving for variable 'l'.

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

Add '-14ln' to each side of the equation.
9ln + -14ln + -4lnx2 = 14ln + -14ln

Combine like terms: 9ln + -14ln = -5ln
-5ln + -4lnx2 = 14ln + -14ln

Combine like terms: 14ln + -14ln = 0
-5ln + -4lnx2 = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(5 + 4x2) = 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 '(5 + 4x2)' equal to zero and attempt to solve:

Simplifying
5 + 4x2 = 0

Solving
5 + 4x2 = 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 + 4x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4x2 = 0 + -5
4x2 = 0 + -5

Combine like terms: 0 + -5 = -5
4x2 = -5

Add '-4x2' to each side of the equation.
4x2 + -4x2 = -5 + -4x2

Combine like terms: 4x2 + -4x2 = 0
0 = -5 + -4x2

Simplifying
0 = -5 + -4x2

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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