log(4x-1)=log(x-6)

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Solution for log(4x-1)=log(x-6) equation: 


Simplifying
log(4x + -1) = log(x + -6)

Reorder the terms:
glo(-1 + 4x) = log(x + -6)
(-1 * glo + 4x * glo) = log(x + -6)
(-1glo + 4glox) = log(x + -6)

Reorder the terms:
-1glo + 4glox = glo(-6 + x)
-1glo + 4glox = (-6 * glo + x * glo)
-1glo + 4glox = (-6glo + glox)

Solving
-1glo + 4glox = -6glo + glox

Solving for variable 'g'.

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

Add '6glo' to each side of the equation.
-1glo + 6glo + 4glox = -6glo + 6glo + glox

Combine like terms: -1glo + 6glo = 5glo
5glo + 4glox = -6glo + 6glo + glox

Combine like terms: -6glo + 6glo = 0
5glo + 4glox = 0 + glox
5glo + 4glox = glox

Add '-1glox' to each side of the equation.
5glo + 4glox + -1glox = glox + -1glox

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

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

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(5 + 3x) = 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 + 3x)' equal to zero and attempt to solve:

Simplifying
5 + 3x = 0

Solving
5 + 3x = 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 + 3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x = 0 + -5
3x = 0 + -5

Combine like terms: 0 + -5 = -5
3x = -5

Add '-3x' to each side of the equation.
3x + -3x = -5 + -3x

Combine like terms: 3x + -3x = 0
0 = -5 + -3x

Simplifying
0 = -5 + -3x

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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