ln(3x+3)=ln(2x-1)*lnx

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Solution for ln(3x+3)=ln(2x-1)*lnx equation: 


Simplifying
ln(3x + 3) = ln(2x + -1) * lnx

Reorder the terms:
ln(3 + 3x) = ln(2x + -1) * lnx
(3 * ln + 3x * ln) = ln(2x + -1) * lnx
(3ln + 3lnx) = ln(2x + -1) * lnx

Reorder the terms:
3ln + 3lnx = ln(-1 + 2x) * lnx

Reorder the terms for easier multiplication:
3ln + 3lnx = ln * lnx(-1 + 2x)

Multiply ln * lnx
3ln + 3lnx = l2n2x(-1 + 2x)
3ln + 3lnx = (-1 * l2n2x + 2x * l2n2x)
3ln + 3lnx = (-1l2n2x + 2l2n2x2)

Solving
3ln + 3lnx = -1l2n2x + 2l2n2x2

Solving for variable 'l'.

Reorder the terms:
3ln + 3lnx + l2n2x + -2l2n2x2 = -1l2n2x + l2n2x + 2l2n2x2 + -2l2n2x2

Combine like terms: -1l2n2x + l2n2x = 0
3ln + 3lnx + l2n2x + -2l2n2x2 = 0 + 2l2n2x2 + -2l2n2x2
3ln + 3lnx + l2n2x + -2l2n2x2 = 2l2n2x2 + -2l2n2x2

Combine like terms: 2l2n2x2 + -2l2n2x2 = 0
3ln + 3lnx + l2n2x + -2l2n2x2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(3 + 3x + lnx + -2lnx2) = 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 + 3x + lnx + -2lnx2)' equal to zero and attempt to solve:

Simplifying
3 + 3x + lnx + -2lnx2 = 0

Reorder the terms:
3 + lnx + -2lnx2 + 3x = 0

Solving
3 + lnx + -2lnx2 + 3x = 0

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

Add '-3' to each side of the equation.
3 + lnx + -2lnx2 + -3 + 3x = 0 + -3

Reorder the terms:
3 + -3 + lnx + -2lnx2 + 3x = 0 + -3

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

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

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

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

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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