g(x)=log(x-1)

Solution for g(x)=log(x-1) equation:

Simplifying
g(x) = log(x + -1)

Multiply g * x
gx = log(x + -1)

Reorder the terms:
gx = glo(-1 + x)
gx = (-1 * glo + x * glo)
gx = (-1glo + glox)

Solving
gx = -1glo + glox

Solving for variable 'g'.

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

Add 'glo' to each side of the equation.
glo + gx = -1glo + glo + glox

Combine like terms: -1glo + glo = 0
glo + gx = 0 + glox
glo + gx = glox

Add '-1glox' to each side of the equation.
glo + -1glox + gx = glox + -1glox

Combine like terms: glox + -1glox = 0
glo + -1glox + gx = 0

Factor out the Greatest Common Factor (GCF), 'g'.
g(lo + -1lox + x) = 0

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

Simplifying
g = 0

Solving
g = 0

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

Simplifying
g = 0
Subproblem 2
Set the factor '(lo + -1lox + x)' equal to zero and attempt to solve:

Simplifying
lo + -1lox + x = 0

Solving
lo + -1lox + x = 0

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

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

Reorder the terms:
lo + -1lo + -1lox + x = 0 + -1lo

Combine like terms: lo + -1lo = 0
0 + -1lox + x = 0 + -1lo
-1lox + x = 0 + -1lo
Remove the zero:
-1lox + x = -1lo

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

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

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

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

Simplifying
0 = -1lo + lox + -1x

The solution to this equation could not be determined.

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