logx+2log(x-1)=2+log(2x+1)

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


Simplifying
logx + 2log(x + -1) = 2 + log(2x + 1)

Reorder the terms:
glox + 2glo(-1 + x) = 2 + log(2x + 1)
glox + (-1 * 2glo + x * 2glo) = 2 + log(2x + 1)
glox + (-2glo + 2glox) = 2 + log(2x + 1)

Reorder the terms:
-2glo + glox + 2glox = 2 + log(2x + 1)

Combine like terms: glox + 2glox = 3glox
-2glo + 3glox = 2 + log(2x + 1)

Reorder the terms:
-2glo + 3glox = 2 + glo(1 + 2x)
-2glo + 3glox = 2 + (1 * glo + 2x * glo)
-2glo + 3glox = 2 + (1glo + 2glox)

Solving
-2glo + 3glox = 2 + 1glo + 2glox

Solving for variable 'g'.

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

Add '-1glo' to each side of the equation.
-2glo + -1glo + 3glox = 2 + 1glo + -1glo + 2glox

Combine like terms: -2glo + -1glo = -3glo
-3glo + 3glox = 2 + 1glo + -1glo + 2glox

Combine like terms: 1glo + -1glo = 0
-3glo + 3glox = 2 + 0 + 2glox
-3glo + 3glox = 2 + 2glox

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

Combine like terms: 3glox + -2glox = 1glox
-3glo + 1glox = 2 + 2glox + -2glox

Combine like terms: 2glox + -2glox = 0
-3glo + 1glox = 2 + 0
-3glo + 1glox = 2

Reorder the terms:
-2 + -3glo + 1glox = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -3glo + 1glox = 0

The solution to this equation could not be determined.

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