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

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


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

Remove parenthesis around (4x)
ln * 4x + -3ln(x) = ln(2)

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

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

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

Combine like terms: 4lnx + -3lnx = 1lnx
1lnx = ln(2)

Reorder the terms for easier multiplication:
1lnx = 2ln

Solving
1lnx = 2ln

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 + 1lnx = 2ln + -2ln

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

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

Simplifying
-2 + x = 0

Solving
-2 + x = 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 + x = 0 + 2

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

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

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

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

Simplifying
0 = 2 + -1x

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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