log(3x-1)=log(4-x)

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Solution for log(3x-1)=log(4-x) equation:


Simplifying
log(3x + -1) = log(4 + -1x)

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

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

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 + -1glox

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

Combine like terms: 4glo + -4glo = 0
-5glo + 3glox = 0 + -1glox
-5glo + 3glox = -1glox

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

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

Combine like terms: -1glox + glox = 0
-5glo + 4glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(-5 + 4x) = 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 '(-5 + 4x)' equal to zero and attempt to solve: Simplifying -5 + 4x = 0 Solving -5 + 4x = 0 Move all terms containing g to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 4x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4x = 0 + 5 4x = 0 + 5 Combine like terms: 0 + 5 = 5 4x = 5 Add '-4x' to each side of the equation. 4x + -4x = 5 + -4x Combine like terms: 4x + -4x = 0 0 = 5 + -4x Simplifying 0 = 5 + -4x 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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