3ln(3a)=ln(9a^3)

Solution for 3ln(3a)=ln(9a^3) equation:

Simplifying
3ln(3a) = ln(9a3)

Remove parenthesis around (3a)
3ln * 3a = ln(9a3)

Reorder the terms for easier multiplication:
3 * 3ln * a = ln(9a3)

Multiply 3 * 3
9ln * a = ln(9a3)

Multiply ln * a
9aln = ln(9a3)

Remove parenthesis around (9a3)
9aln = ln * 9a3

Reorder the terms for easier multiplication:
9aln = 9ln * a3

Multiply ln * a3
9aln = 9a3ln

Solving
9aln = 9a3ln

Solving for variable 'a'.

Combine like terms: 9a3ln + -9a3ln = 0
9aln + -9a3ln = 0

Factor out the Greatest Common Factor (GCF), '9aln'.
9aln(1 + -1a2) = 0

Factor a difference between two squares.
9aln((1 + a)(1 + -1a)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor 'aln' equal to zero and attempt to solve:

Simplifying
aln = 0

Solving
aln = 0

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

Simplifying
aln = 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 '(1 + a)' equal to zero and attempt to solve:

Simplifying
1 + a = 0

Solving
1 + a = 0

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

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

Combine like terms: 1 + -1 = 0
0 + a = 0 + -1
a = 0 + -1

Combine like terms: 0 + -1 = -1
a = -1

Simplifying
a = -1
Subproblem 3
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1a = 0 + -1
-1a = 0 + -1

Combine like terms: 0 + -1 = -1
-1a = -1

Divide each side by '-1'.
a = 1

Simplifying
a = 1
Solution
a = {-1, 1}