2*ln(x)=ln(2)+ln(3x-4)

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


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

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

Reorder the terms for easier multiplication:
2lnx = 2ln + ln(3x + -4)

Reorder the terms:
2lnx = 2ln + ln(-4 + 3x)
2lnx = 2ln + (-4 * ln + 3x * ln)
2lnx = 2ln + (-4ln + 3lnx)

Combine like terms: 2ln + -4ln = -2ln
2lnx = -2ln + 3lnx

Solving
2lnx = -2ln + 3lnx

Solving for variable 'l'.

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(2 + -1x) = 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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Add 'x' to each side of the equation.
-1x + x = -2 + x

Combine like terms: -1x + x = 0
0 = -2 + x

Simplifying
0 = -2 + x

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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