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

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


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

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

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

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

Combine like terms: -1glo + -4glo = -5glo
-5glo + 2glox + glox = log(x + -2)

Combine like terms: 2glox + glox = 3glox
-5glo + 3glox = log(x + -2)

Reorder the terms:
-5glo + 3glox = glo(-2 + x)
-5glo + 3glox = (-2 * glo + x * glo)
-5glo + 3glox = (-2glo + glox)

Solving
-5glo + 3glox = -2glo + glox

Solving for variable 'g'.

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

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

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

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

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

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

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

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

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 '(-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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