log[5](9x+5)-log[5](x-3)=2

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Solution for log[5](9x+5)-log[5](x-3)=2 equation:


Simplifying
log[5](9x + 5) + -1log[5](x + -3) = 2

Reorder the terms:
glo * 5(5 + 9x) + -1log[5](x + -3) = 2

Reorder the terms for easier multiplication:
5glo(5 + 9x) + -1log[5](x + -3) = 2
(5 * 5glo + 9x * 5glo) + -1log[5](x + -3) = 2
(25glo + 45glox) + -1log[5](x + -3) = 2

Reorder the terms:
25glo + 45glox + -1glo * 5(-3 + x) = 2

Reorder the terms for easier multiplication:
25glo + 45glox + -1 * 5glo(-3 + x) = 2

Multiply -1 * 5
25glo + 45glox + -5glo(-3 + x) = 2
25glo + 45glox + (-3 * -5glo + x * -5glo) = 2
25glo + 45glox + (15glo + -5glox) = 2

Reorder the terms:
25glo + 15glo + 45glox + -5glox = 2

Combine like terms: 25glo + 15glo = 40glo
40glo + 45glox + -5glox = 2

Combine like terms: 45glox + -5glox = 40glox
40glo + 40glox = 2

Solving
40glo + 40glox = 2

Solving for variable 'g'.

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

Reorder the terms:
-2 + 40glo + 40glox = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 40glo + 40glox = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 20glo + 20glox) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + 20glo + 20glox)' equal to zero and attempt to solve: Simplifying -1 + 20glo + 20glox = 0 Solving -1 + 20glo + 20glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 20glo + 1 + 20glox = 0 + 1 Reorder the terms: -1 + 1 + 20glo + 20glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 20glo + 20glox = 0 + 1 20glo + 20glox = 0 + 1 Combine like terms: 0 + 1 = 1 20glo + 20glox = 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.

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