log(2x-1)+log(x+2)=log(8x-4)

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Solution for log(2x-1)+log(x+2)=log(8x-4) equation:


Simplifying
log(2x + -1) + log(x + 2) = log(8x + -4)

Reorder the terms:
glo(-1 + 2x) + log(x + 2) = log(8x + -4)
(-1 * glo + 2x * glo) + log(x + 2) = log(8x + -4)
(-1glo + 2glox) + log(x + 2) = log(8x + -4)

Reorder the terms:
-1glo + 2glox + glo(2 + x) = log(8x + -4)
-1glo + 2glox + (2 * glo + x * glo) = log(8x + -4)
-1glo + 2glox + (2glo + glox) = log(8x + -4)

Reorder the terms:
-1glo + 2glo + 2glox + glox = log(8x + -4)

Combine like terms: -1glo + 2glo = 1glo
1glo + 2glox + glox = log(8x + -4)

Combine like terms: 2glox + glox = 3glox
1glo + 3glox = log(8x + -4)

Reorder the terms:
1glo + 3glox = glo(-4 + 8x)
1glo + 3glox = (-4 * glo + 8x * glo)
1glo + 3glox = (-4glo + 8glox)

Solving
1glo + 3glox = -4glo + 8glox

Solving for variable 'g'.

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

Add '4glo' to each side of the equation.
1glo + 4glo + 3glox = -4glo + 4glo + 8glox

Combine like terms: 1glo + 4glo = 5glo
5glo + 3glox = -4glo + 4glo + 8glox

Combine like terms: -4glo + 4glo = 0
5glo + 3glox = 0 + 8glox
5glo + 3glox = 8glox

Add '-8glox' to each side of the equation.
5glo + 3glox + -8glox = 8glox + -8glox

Combine like terms: 3glox + -8glox = -5glox
5glo + -5glox = 8glox + -8glox

Combine like terms: 8glox + -8glox = 0
5glo + -5glox = 0

Factor out the Greatest Common Factor (GCF), '5glo'.
5glo(1 + -1x) = 0

Ignore the factor 5.

Subproblem 1

Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x 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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