g(x)=log(3)(2x+1)

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Solution for g(x)=log(3)(2x+1) equation: 


Simplifying
g(x) = log(3)(2x + 1)

Multiply g * x
gx = log(3)(2x + 1)

Reorder the terms:
gx = glo * 3(1 + 2x)

Reorder the terms for easier multiplication:
gx = 3glo(1 + 2x)
gx = (1 * 3glo + 2x * 3glo)
gx = (3glo + 6glox)

Solving
gx = 3glo + 6glox

Solving for variable 'g'.

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

Add '-3glo' to each side of the equation.
-3glo + gx = 3glo + -3glo + 6glox

Combine like terms: 3glo + -3glo = 0
-3glo + gx = 0 + 6glox
-3glo + gx = 6glox

Add '-6glox' to each side of the equation.
-3glo + -6glox + gx = 6glox + -6glox

Combine like terms: 6glox + -6glox = 0
-3glo + -6glox + gx = 0

Factor out the Greatest Common Factor (GCF), 'g'.
g(-3lo + -6lox + x) = 0


Subproblem 1
Set the factor 'g' equal to zero and attempt to solve:

Simplifying
g = 0

Solving
g = 0

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

Simplifying
g = 0

Subproblem 2
Set the factor '(-3lo + -6lox + x)' equal to zero and attempt to solve:

Simplifying
-3lo + -6lox + x = 0

Solving
-3lo + -6lox + x = 0

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

Add '3lo' to each side of the equation.
-3lo + -6lox + 3lo + x = 0 + 3lo

Reorder the terms:
-3lo + 3lo + -6lox + x = 0 + 3lo

Combine like terms: -3lo + 3lo = 0
0 + -6lox + x = 0 + 3lo
-6lox + x = 0 + 3lo
Remove the zero:
-6lox + x = 3lo

Add '6lox' to each side of the equation.
-6lox + 6lox + x = 3lo + 6lox

Combine like terms: -6lox + 6lox = 0
0 + x = 3lo + 6lox
x = 3lo + 6lox

Add '-1x' to each side of the equation.
x + -1x = 3lo + 6lox + -1x

Combine like terms: x + -1x = 0
0 = 3lo + 6lox + -1x

Simplifying
0 = 3lo + 6lox + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
g = {0}

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