log[7](1+3x)=log[7]2

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Solution for log[7](1+3x)=log[7]2 equation: 


Simplifying
log[7](1 + 3x) = log[7] * 2

Reorder the terms for easier multiplication:
7glo(1 + 3x) = log[7] * 2
(1 * 7glo + 3x * 7glo) = log[7] * 2
(7glo + 21glox) = log[7] * 2

Reorder the terms for easier multiplication:
7glo + 21glox = 7 * 2glo

Multiply 7 * 2
7glo + 21glox = 14glo

Solving
7glo + 21glox = 14glo

Solving for variable 'g'.

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

Add '-14glo' to each side of the equation.
7glo + -14glo + 21glox = 14glo + -14glo

Combine like terms: 7glo + -14glo = -7glo
-7glo + 21glox = 14glo + -14glo

Combine like terms: 14glo + -14glo = 0
-7glo + 21glox = 0

Factor out the Greatest Common Factor (GCF), '7glo'.
7glo(-1 + 3x) = 0

Ignore the factor 7.

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 + 3x)' equal to zero and attempt to solve:

Simplifying
-1 + 3x = 0

Solving
-1 + 3x = 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 + 3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3x = 0 + 1
3x = 0 + 1

Combine like terms: 0 + 1 = 1
3x = 1

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

Combine like terms: 3x + -3x = 0
0 = 1 + -3x

Simplifying
0 = 1 + -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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