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

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


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

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

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

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

Combine like terms: 6ln + -1ln = 5ln
nxL = 5ln + -2lnx

Solving
nxL = 5ln + -2lnx

Solving for variable 'n'.

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

Add '-5ln' to each side of the equation.
-5ln + nxL = 5ln + -5ln + -2lnx

Combine like terms: 5ln + -5ln = 0
-5ln + nxL = 0 + -2lnx
-5ln + nxL = -2lnx

Add '2lnx' to each side of the equation.
-5ln + 2lnx + nxL = -2lnx + 2lnx

Combine like terms: -2lnx + 2lnx = 0
-5ln + 2lnx + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-5l + 2lx + xL) = 0


Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(-5l + 2lx + xL)' equal to zero and attempt to solve:

Simplifying
-5l + 2lx + xL = 0

Solving
-5l + 2lx + xL = 0

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

Add '5l' to each side of the equation.
-5l + 2lx + 5l + xL = 0 + 5l

Reorder the terms:
-5l + 5l + 2lx + xL = 0 + 5l

Combine like terms: -5l + 5l = 0
0 + 2lx + xL = 0 + 5l
2lx + xL = 0 + 5l
Remove the zero:
2lx + xL = 5l

Add '-2lx' to each side of the equation.
2lx + -2lx + xL = 5l + -2lx

Combine like terms: 2lx + -2lx = 0
0 + xL = 5l + -2lx
xL = 5l + -2lx

Add '-1xL' to each side of the equation.
xL + -1xL = 5l + -2lx + -1xL

Combine like terms: xL + -1xL = 0
0 = 5l + -2lx + -1xL

Simplifying
0 = 5l + -2lx + -1xL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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