log(x+5)=log(5x)

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Solution for log(x+5)=log(5x) equation: 


Simplifying
log(x + 5) = log(5x)

Reorder the terms:
glo(5 + x) = log(5x)
(5 * glo + x * glo) = log(5x)
(5glo + glox) = log(5x)

Remove parenthesis around (5x)
5glo + glox = glo * 5x

Reorder the terms for easier multiplication:
5glo + glox = 5glo * x

Multiply glo * x
5glo + glox = 5glox

Solving
5glo + glox = 5glox

Solving for variable 'g'.

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

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

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

Combine like terms: 5glox + -5glox = 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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