In(7x-1)+in(2)=in(x-7)

Solution for In(7x-1)+in(2)=in(x-7) equation:

Simplifying
In(7x + -1) + in(2) = in(x + -7)

Reorder the terms:
nI(-1 + 7x) + in(2) = in(x + -7)
(-1 * nI + 7x * nI) + in(2) = in(x + -7)
(-1nI + 7nxI) + in(2) = in(x + -7)

Reorder the terms for easier multiplication:
-1nI + 7nxI + 2in = in(x + -7)

Reorder the terms:
2in + -1nI + 7nxI = in(x + -7)

Reorder the terms:
2in + -1nI + 7nxI = in(-7 + x)
2in + -1nI + 7nxI = (-7 * in + x * in)
2in + -1nI + 7nxI = (-7in + inx)

Solving
2in + -1nI + 7nxI = -7in + inx

Solving for variable 'i'.

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

Add '7in' to each side of the equation.
2in + -1nI + 7in + 7nxI = -7in + 7in + inx

Reorder the terms:
2in + 7in + -1nI + 7nxI = -7in + 7in + inx

Combine like terms: 2in + 7in = 9in
9in + -1nI + 7nxI = -7in + 7in + inx

Combine like terms: -7in + 7in = 0
9in + -1nI + 7nxI = 0 + inx
9in + -1nI + 7nxI = inx

Add '-1inx' to each side of the equation.
9in + -1nI + -1inx + 7nxI = inx + -1inx

Reorder the terms:
9in + -1inx + -1nI + 7nxI = inx + -1inx

Combine like terms: inx + -1inx = 0
9in + -1inx + -1nI + 7nxI = 0

Add 'nI' to each side of the equation.
9in + -1inx + -1nI + nI + 7nxI = 0 + nI

Combine like terms: -1nI + nI = 0
9in + -1inx + 0 + 7nxI = 0 + nI
9in + -1inx + 7nxI = 0 + nI
Remove the zero:
9in + -1inx + 7nxI = nI

Add '-7nxI' to each side of the equation.
9in + -1inx + 7nxI + -7nxI = nI + -7nxI

Combine like terms: 7nxI + -7nxI = 0
9in + -1inx + 0 = nI + -7nxI
9in + -1inx = nI + -7nxI

Reorder the terms:
9in + -1inx + -1nI + 7nxI = nI + -1nI + -7nxI + 7nxI

Combine like terms: nI + -1nI = 0
9in + -1inx + -1nI + 7nxI = 0 + -7nxI + 7nxI
9in + -1inx + -1nI + 7nxI = -7nxI + 7nxI

Combine like terms: -7nxI + 7nxI = 0
9in + -1inx + -1nI + 7nxI = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(9i + -1ix + -1I + 7xI) = 0

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

Simplifying
n = 0

Solving
n = 0

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

Add '-1n' to each side of the equation.
n + -1n = 0 + -1n
Remove the zero:
0 = -1n

Simplifying
0 = -1n

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 '(9i + -1ix + -1I + 7xI)' equal to zero and attempt to solve:

Simplifying
9i + -1ix + -1I + 7xI = 0

Reorder the terms:
-1I + 9i + -1ix + 7xI = 0

Solving
-1I + 9i + -1ix + 7xI = 0

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

Add 'I' to each side of the equation.
-1I + 9i + -1ix + I + 7xI = 0 + I

Reorder the terms:
-1I + I + 9i + -1ix + 7xI = 0 + I

Combine like terms: -1I + I = 0
0 + 9i + -1ix + 7xI = 0 + I
9i + -1ix + 7xI = 0 + I
Remove the zero:
9i + -1ix + 7xI = I

Add '-7xI' to each side of the equation.
9i + -1ix + 7xI + -7xI = I + -7xI

Combine like terms: 7xI + -7xI = 0
9i + -1ix + 0 = I + -7xI
9i + -1ix = I + -7xI

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.