log(x-3)+log(x+2)=log(4x)

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Solution for log(x-3)+log(x+2)=log(4x) equation:


Simplifying
log(x + -3) + log(x + 2) = log(4x)

Reorder the terms:
glo(-3 + x) + log(x + 2) = log(4x)
(-3 * glo + x * glo) + log(x + 2) = log(4x)
(-3glo + glox) + log(x + 2) = log(4x)

Reorder the terms:
-3glo + glox + glo(2 + x) = log(4x)
-3glo + glox + (2 * glo + x * glo) = log(4x)
-3glo + glox + (2glo + glox) = log(4x)

Reorder the terms:
-3glo + 2glo + glox + glox = log(4x)

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

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

Remove parenthesis around (4x)
-1glo + 2glox = glo * 4x

Reorder the terms for easier multiplication:
-1glo + 2glox = 4glo * x

Multiply glo * x
-1glo + 2glox = 4glox

Solving
-1glo + 2glox = 4glox

Solving for variable 'g'.

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

Add '-4glox' to each side of the equation.
-1glo + 2glox + -4glox = 4glox + -4glox

Combine like terms: 2glox + -4glox = -2glox
-1glo + -2glox = 4glox + -4glox

Combine like terms: 4glox + -4glox = 0
-1glo + -2glox = 0

Factor out the Greatest Common Factor (GCF), '-1glo'.
-1glo(1 + 2x) = 0

Ignore the factor -1.

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 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -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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