3ln(x)-4=ln(6x^2)+2

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Solution for 3ln(x)-4=ln(6x^2)+2 equation: 


Simplifying
3ln(x) + -4 = ln(6x2) + 2

Multiply ln * x
3lnx + -4 = ln(6x2) + 2

Reorder the terms:
-4 + 3lnx = ln(6x2) + 2

Remove parenthesis around (6x2)
-4 + 3lnx = ln * 6x2 + 2

Reorder the terms for easier multiplication:
-4 + 3lnx = 6ln * x2 + 2

Multiply ln * x2
-4 + 3lnx = 6lnx2 + 2

Reorder the terms:
-4 + 3lnx = 2 + 6lnx2

Solving
-4 + 3lnx = 2 + 6lnx2

Solving for variable 'l'.

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

Add '-6lnx2' to each side of the equation.
-4 + 3lnx + -6lnx2 = 2 + 6lnx2 + -6lnx2

Combine like terms: 6lnx2 + -6lnx2 = 0
-4 + 3lnx + -6lnx2 = 2 + 0
-4 + 3lnx + -6lnx2 = 2

Add '4' to each side of the equation.
-4 + 3lnx + 4 + -6lnx2 = 2 + 4

Reorder the terms:
-4 + 4 + 3lnx + -6lnx2 = 2 + 4

Combine like terms: -4 + 4 = 0
0 + 3lnx + -6lnx2 = 2 + 4
3lnx + -6lnx2 = 2 + 4

Combine like terms: 2 + 4 = 6
3lnx + -6lnx2 = 6

Reorder the terms:
-6 + 3lnx + -6lnx2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 3lnx + -6lnx2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + lnx + -2lnx2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-2 + lnx + -2lnx2)' equal to zero and attempt to solve:

Simplifying
-2 + lnx + -2lnx2 = 0

Solving
-2 + lnx + -2lnx2 = 0

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

Add '2' to each side of the equation.
-2 + lnx + 2 + -2lnx2 = 0 + 2

Reorder the terms:
-2 + 2 + lnx + -2lnx2 = 0 + 2

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

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

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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