ln(3)=ln(6)+ln(a)+3a^2

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Solution for ln(3)=ln(6)+ln(a)+3a^2 equation: 


Simplifying
ln(3) = ln(6) + ln(a) + 3a2

Reorder the terms for easier multiplication:
3ln = ln(6) + ln(a) + 3a2

Reorder the terms for easier multiplication:
3ln = 6ln + ln(a) + 3a2

Multiply ln * a
3ln = 6ln + aln + 3a2

Reorder the terms:
3ln = aln + 3a2 + 6ln

Solving
3ln = aln + 3a2 + 6ln

Solving for variable 'l'.

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

Add '-1aln' to each side of the equation.
-1aln + 3ln = aln + 3a2 + -1aln + 6ln

Reorder the terms:
-1aln + 3ln = aln + -1aln + 3a2 + 6ln

Combine like terms: aln + -1aln = 0
-1aln + 3ln = 0 + 3a2 + 6ln
-1aln + 3ln = 3a2 + 6ln

Add '-6ln' to each side of the equation.
-1aln + 3ln + -6ln = 3a2 + 6ln + -6ln

Combine like terms: 3ln + -6ln = -3ln
-1aln + -3ln = 3a2 + 6ln + -6ln

Combine like terms: 6ln + -6ln = 0
-1aln + -3ln = 3a2 + 0
-1aln + -3ln = 3a2

Reorder the terms:
-1aln + -3a2 + -3ln = 3a2 + -3a2

Combine like terms: 3a2 + -3a2 = 0
-1aln + -3a2 + -3ln = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(aln + 3a2 + 3ln) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(aln + 3a2 + 3ln)' equal to zero and attempt to solve:

Simplifying
aln + 3a2 + 3ln = 0

Solving
aln + 3a2 + 3ln = 0

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

Add '-3a2' to each side of the equation.
aln + 3a2 + -3a2 + 3ln = 0 + -3a2

Combine like terms: 3a2 + -3a2 = 0
aln + 0 + 3ln = 0 + -3a2
aln + 3ln = 0 + -3a2
Remove the zero:
aln + 3ln = -3a2

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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