log(3x+1)=log(5x)

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Solution for log(3x+1)=log(5x) equation: 


Simplifying
log(3x + 1) = log(5x)

Reorder the terms:
glo(1 + 3x) = log(5x)
(1 * glo + 3x * glo) = log(5x)
(1glo + 3glox) = log(5x)

Remove parenthesis around (5x)
1glo + 3glox = glo * 5x

Reorder the terms for easier multiplication:
1glo + 3glox = 5glo * x

Multiply glo * x
1glo + 3glox = 5glox

Solving
1glo + 3glox = 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.
1glo + 3glox + -5glox = 5glox + -5glox

Combine like terms: 3glox + -5glox = -2glox
1glo + -2glox = 5glox + -5glox

Combine like terms: 5glox + -5glox = 0
1glo + -2glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(1 + -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 '(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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