log[5]10-log[5](1-3x)=3

Solution for log[5]10-log[5](1-3x)=3 equation:

Simplifying
log[5] * 10 + -1log[5](1 + -3x) = 3

Reorder the terms for easier multiplication:
5 * 10glo + -1log[5](1 + -3x) = 3

Multiply 5 * 10
50glo + -1log[5](1 + -3x) = 3

Reorder the terms for easier multiplication:
50glo + -1 * 5glo(1 + -3x) = 3

Multiply -1 * 5
50glo + -5glo(1 + -3x) = 3
50glo + (1 * -5glo + -3x * -5glo) = 3
50glo + (-5glo + 15glox) = 3

Combine like terms: 50glo + -5glo = 45glo
45glo + 15glox = 3

Solving
45glo + 15glox = 3

Solving for variable 'g'.

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

Reorder the terms:
-3 + 45glo + 15glox = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 45glo + 15glox = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 15glo + 5glox) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + 15glo + 5glox)' equal to zero and attempt to solve:

Simplifying
-1 + 15glo + 5glox = 0

Solving
-1 + 15glo + 5glox = 0

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

Add '1' to each side of the equation.
-1 + 15glo + 1 + 5glox = 0 + 1

Reorder the terms:
-1 + 1 + 15glo + 5glox = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 15glo + 5glox = 0 + 1
15glo + 5glox = 0 + 1

Combine like terms: 0 + 1 = 1
15glo + 5glox = 1

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.