ln(7x^2+1)-3ln(x)=ln(8)

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Solution for ln(7x^2+1)-3ln(x)=ln(8) equation: 


Simplifying
ln(7x2 + 1) + -3ln(x) = ln(8)

Reorder the terms:
ln(1 + 7x2) + -3ln(x) = ln(8)
(1 * ln + 7x2 * ln) + -3ln(x) = ln(8)
(1ln + 7lnx2) + -3ln(x) = ln(8)

Multiply ln * x
1ln + 7lnx2 + -3lnx = ln(8)

Reorder the terms:
1ln + -3lnx + 7lnx2 = ln(8)

Reorder the terms for easier multiplication:
1ln + -3lnx + 7lnx2 = 8ln

Solving
1ln + -3lnx + 7lnx2 = 8ln

Solving for variable 'l'.

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

Add '-8ln' to each side of the equation.
1ln + -3lnx + -8ln + 7lnx2 = 8ln + -8ln

Reorder the terms:
1ln + -8ln + -3lnx + 7lnx2 = 8ln + -8ln

Combine like terms: 1ln + -8ln = -7ln
-7ln + -3lnx + 7lnx2 = 8ln + -8ln

Combine like terms: 8ln + -8ln = 0
-7ln + -3lnx + 7lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-7 + -3x + 7x2) = 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 + -3x + 7x2)' equal to zero and attempt to solve:

Simplifying
-7 + -3x + 7x2 = 0

Solving
-7 + -3x + 7x2 = 0

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

Add '7' to each side of the equation.
-7 + -3x + 7 + 7x2 = 0 + 7

Reorder the terms:
-7 + 7 + -3x + 7x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3x + 7x2 = 0 + 7
-3x + 7x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-3x + 7x2 = 7

Add '3x' to each side of the equation.
-3x + 3x + 7x2 = 7 + 3x

Combine like terms: -3x + 3x = 0
0 + 7x2 = 7 + 3x
7x2 = 7 + 3x

Add '-7x2' to each side of the equation.
7x2 + -7x2 = 7 + 3x + -7x2

Combine like terms: 7x2 + -7x2 = 0
0 = 7 + 3x + -7x2

Simplifying
0 = 7 + 3x + -7x2

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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