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

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


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

Reorder the terms:
ln(-14 + x2) = ln(7 + -4x)
(-14 * ln + x2 * ln) = ln(7 + -4x)
(-14ln + lnx2) = ln(7 + -4x)
-14ln + lnx2 = (7 * ln + -4x * ln)
-14ln + lnx2 = (7ln + -4lnx)

Solving
-14ln + lnx2 = 7ln + -4lnx

Solving for variable 'l'.

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

Add '-7ln' to each side of the equation.
-14ln + -7ln + lnx2 = 7ln + -7ln + -4lnx

Combine like terms: -14ln + -7ln = -21ln
-21ln + lnx2 = 7ln + -7ln + -4lnx

Combine like terms: 7ln + -7ln = 0
-21ln + lnx2 = 0 + -4lnx
-21ln + lnx2 = -4lnx

Add '4lnx' to each side of the equation.
-21ln + 4lnx + lnx2 = -4lnx + 4lnx

Combine like terms: -4lnx + 4lnx = 0
-21ln + 4lnx + lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-21 + 4x + x2) = 0

Factor a trinomial.
ln((-7 + -1x)(3 + -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 '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Add 'x' to each side of the equation.
-1x + x = 7 + x

Combine like terms: -1x + x = 0
0 = 7 + x

Simplifying
0 = 7 + 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 '(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.

The solution to this equation could not be determined.

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