ln(x)=ln(2)-ln(6x-1)

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Solution for ln(x)=ln(2)-ln(6x-1) equation: 


Simplifying
ln(x) = ln(2) + -1ln(6x + -1)

Multiply ln * x
lnx = ln(2) + -1ln(6x + -1)

Reorder the terms for easier multiplication:
lnx = 2ln + -1ln(6x + -1)

Reorder the terms:
lnx = 2ln + -1ln(-1 + 6x)
lnx = 2ln + (-1 * -1ln + 6x * -1ln)
lnx = 2ln + (1ln + -6lnx)

Combine like terms: 2ln + 1ln = 3ln
lnx = 3ln + -6lnx

Solving
lnx = 3ln + -6lnx

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
-3ln + lnx = 3ln + -3ln + -6lnx

Combine like terms: 3ln + -3ln = 0
-3ln + lnx = 0 + -6lnx
-3ln + lnx = -6lnx

Add '6lnx' to each side of the equation.
-3ln + lnx + 6lnx = -6lnx + 6lnx

Combine like terms: lnx + 6lnx = 7lnx
-3ln + 7lnx = -6lnx + 6lnx

Combine like terms: -6lnx + 6lnx = 0
-3ln + 7lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-3 + 7x) = 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 + 7x)' equal to zero and attempt to solve:

Simplifying
-3 + 7x = 0

Solving
-3 + 7x = 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 + 7x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 7x = 0 + 3
7x = 0 + 3

Combine like terms: 0 + 3 = 3
7x = 3

Add '-7x' to each side of the equation.
7x + -7x = 3 + -7x

Combine like terms: 7x + -7x = 0
0 = 3 + -7x

Simplifying
0 = 3 + -7x

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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