log(5x+2)-1=log(2x-1)

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Solution for log(5x+2)-1=log(2x-1) equation:


Simplifying
log(5x + 2) + -1 = log(2x + -1)

Reorder the terms:
glo(2 + 5x) + -1 = log(2x + -1)
(2 * glo + 5x * glo) + -1 = log(2x + -1)
(2glo + 5glox) + -1 = log(2x + -1)

Reorder the terms:
-1 + 2glo + 5glox = log(2x + -1)

Reorder the terms:
-1 + 2glo + 5glox = glo(-1 + 2x)
-1 + 2glo + 5glox = (-1 * glo + 2x * glo)
-1 + 2glo + 5glox = (-1glo + 2glox)

Solving
-1 + 2glo + 5glox = -1glo + 2glox

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.
-1 + 2glo + glo + 5glox = -1glo + glo + 2glox

Combine like terms: 2glo + glo = 3glo
-1 + 3glo + 5glox = -1glo + glo + 2glox

Combine like terms: -1glo + glo = 0
-1 + 3glo + 5glox = 0 + 2glox
-1 + 3glo + 5glox = 2glox

Add '-2glox' to each side of the equation.
-1 + 3glo + 5glox + -2glox = 2glox + -2glox

Combine like terms: 5glox + -2glox = 3glox
-1 + 3glo + 3glox = 2glox + -2glox

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

Add '1' to each side of the equation.
-1 + 3glo + 1 + 3glox = 0 + 1

Reorder the terms:
-1 + 1 + 3glo + 3glox = 0 + 1

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

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

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

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

The solution to this equation could not be determined.

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