on(3x+1)=lnx

Solution for on(3x+1)=lnx equation:

Simplifying
on(3x + 1) = lnx

Reorder the terms:
no(1 + 3x) = lnx
(1 * no + 3x * no) = lnx
(1no + 3nox) = lnx

Solving
1no + 3nox = lnx

Solving for variable 'n'.

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

Add '-1lnx' to each side of the equation.
1no + -1lnx + 3nox = lnx + -1lnx

Reorder the terms:
-1lnx + 1no + 3nox = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-1lnx + 1no + 3nox = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-1lx + o + 3ox) = 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 '(-1lx + o + 3ox)' equal to zero and attempt to solve:

Simplifying
-1lx + o + 3ox = 0

Solving
-1lx + o + 3ox = 0

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

Add 'lx' to each side of the equation.
-1lx + o + lx + 3ox = 0 + lx

Reorder the terms:
-1lx + lx + o + 3ox = 0 + lx

Combine like terms: -1lx + lx = 0
0 + o + 3ox = 0 + lx
o + 3ox = 0 + lx
Remove the zero:
o + 3ox = lx

Add '-1o' to each side of the equation.
o + -1o + 3ox = lx + -1o

Combine like terms: o + -1o = 0
0 + 3ox = lx + -1o
3ox = lx + -1o

Add '-3ox' to each side of the equation.
3ox + -3ox = lx + -1o + -3ox

Combine like terms: 3ox + -3ox = 0
0 = lx + -1o + -3ox

Simplifying
0 = lx + -1o + -3ox

The solution to this equation could not be determined.

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