Lg(x+1)=2lgx

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Solution for Lg(x+1)=2lgx equation: 


Simplifying
Lg(x + 1) = 2lgx

Reorder the terms:
gL(1 + x) = 2lgx
(1 * gL + x * gL) = 2lgx
(1gL + gxL) = 2lgx

Solving
1gL + gxL = 2glx

Solving for variable 'g'.

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

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

Combine like terms: 2glx + -2glx = 0
1gL + -2glx + gxL = 0

Factor out the Greatest Common Factor (GCF), 'g'.
g(L + -2lx + xL) = 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 '(L + -2lx + xL)' equal to zero and attempt to solve:

Simplifying
L + -2lx + xL = 0

Solving
L + -2lx + xL = 0

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

Add '-1L' to each side of the equation.
L + -2lx + -1L + xL = 0 + -1L

Reorder the terms:
L + -1L + -2lx + xL = 0 + -1L

Combine like terms: L + -1L = 0
0 + -2lx + xL = 0 + -1L
-2lx + xL = 0 + -1L
Remove the zero:
-2lx + xL = -1L

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

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

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

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

Simplifying
0 = -1L + 2lx + -1xL

The solution to this equation could not be determined.

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

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