ln(4*x)-6*ln(x)=ln(2)

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Solution for ln(4*x)-6*ln(x)=ln(2) equation: 


Simplifying
ln(4x) + -6ln(x) = ln(2)

Remove parenthesis around (4x)
ln * 4x + -6ln(x) = ln(2)

Reorder the terms for easier multiplication:
4ln * x + -6ln(x) = ln(2)

Multiply ln * x
4lnx + -6ln(x) = ln(2)

Multiply ln * x
4lnx + -6lnx = ln(2)

Combine like terms: 4lnx + -6lnx = -2lnx
-2lnx = ln(2)

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

Solving
-2lnx = 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 + -2lnx = 2ln + -2ln

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

Factor out the Greatest Common Factor (GCF), '-2ln'.
-2ln(1 + x) = 0

Ignore the factor -2.

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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

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

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

Simplifying
0 = -1 + -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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