lg(x)+lg(x-1)=lg(2)

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Solution for lg(x)+lg(x-1)=lg(2) equation: 


Simplifying
lg(x) + lg(x + -1) = lg(2)

Multiply gl * x
glx + lg(x + -1) = lg(2)

Reorder the terms:
glx + gl(-1 + x) = lg(2)
glx + (-1 * gl + x * gl) = lg(2)
glx + (-1gl + glx) = lg(2)

Reorder the terms:
-1gl + glx + glx = lg(2)

Combine like terms: glx + glx = 2glx
-1gl + 2glx = lg(2)

Reorder the terms for easier multiplication:
-1gl + 2glx = 2gl

Solving
-1gl + 2glx = 2gl

Solving for variable 'g'.

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

Add '-2gl' to each side of the equation.
-1gl + -2gl + 2glx = 2gl + -2gl

Combine like terms: -1gl + -2gl = -3gl
-3gl + 2glx = 2gl + -2gl

Combine like terms: 2gl + -2gl = 0
-3gl + 2glx = 0

Factor out the Greatest Common Factor (GCF), 'gl'.
gl(-3 + 2x) = 0


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

Simplifying
gl = 0

Solving
gl = 0

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

Simplifying
gl = 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 + 2x)' equal to zero and attempt to solve:

Simplifying
-3 + 2x = 0

Solving
-3 + 2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + 2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2x = 0 + 3
2x = 0 + 3

Combine like terms: 0 + 3 = 3
2x = 3

Add '-2x' to each side of the equation.
2x + -2x = 3 + -2x

Combine like terms: 2x + -2x = 0
0 = 3 + -2x

Simplifying
0 = 3 + -2x

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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