ln(3)=ln(16x)*4x^2

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Solution for ln(3)=ln(16x)*4x^2 equation: 


Simplifying
ln(3) = ln(16x) * 4x2

Reorder the terms for easier multiplication:
3ln = ln(16x) * 4x2

Remove parenthesis around (16x)
3ln = ln * 16x * 4x2

Reorder the terms for easier multiplication:
3ln = 16 * 4ln * x * x2

Multiply 16 * 4
3ln = 64ln * x * x2

Multiply ln * x
3ln = 64lnx * x2

Multiply lnx * x2
3ln = 64lnx3

Solving
3ln = 64lnx3

Solving for variable 'l'.

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

Add '-64lnx3' to each side of the equation.
3ln + -64lnx3 = 64lnx3 + -64lnx3

Combine like terms: 64lnx3 + -64lnx3 = 0
3ln + -64lnx3 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(3 + -64x3) = 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 '(3 + -64x3)' equal to zero and attempt to solve:

Simplifying
3 + -64x3 = 0

Solving
3 + -64x3 = 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 + -64x3 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -64x3 = 0 + -3
-64x3 = 0 + -3

Combine like terms: 0 + -3 = -3
-64x3 = -3

Add '64x3' to each side of the equation.
-64x3 + 64x3 = -3 + 64x3

Combine like terms: -64x3 + 64x3 = 0
0 = -3 + 64x3

Simplifying
0 = -3 + 64x3

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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