(2)log[9]x=log[9](x+15)+log[9]4

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Solution for (2)log[9]x=log[9](x+15)+log[9]4 equation:


Simplifying
(2) * log[9] * x = log[9](x + 15) + log[9] * 4

Reorder the terms for easier multiplication:
2 * 9glo * x = log[9](x + 15) + log[9] * 4

Multiply 2 * 9
18glo * x = log[9](x + 15) + log[9] * 4

Multiply glo * x
18glox = log[9](x + 15) + log[9] * 4

Reorder the terms:
18glox = glo * 9(15 + x) + log[9] * 4

Reorder the terms for easier multiplication:
18glox = 9glo(15 + x) + log[9] * 4
18glox = (15 * 9glo + x * 9glo) + log[9] * 4
18glox = (135glo + 9glox) + log[9] * 4

Reorder the terms for easier multiplication:
18glox = 135glo + 9glox + 9 * 4glo

Multiply 9 * 4
18glox = 135glo + 9glox + 36glo

Reorder the terms:
18glox = 135glo + 36glo + 9glox

Combine like terms: 135glo + 36glo = 171glo
18glox = 171glo + 9glox

Solving
18glox = 171glo + 9glox

Solving for variable 'g'.

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

Add '-171glo' to each side of the equation.
-171glo + 18glox = 171glo + -171glo + 9glox

Combine like terms: 171glo + -171glo = 0
-171glo + 18glox = 0 + 9glox
-171glo + 18glox = 9glox

Add '-9glox' to each side of the equation.
-171glo + 18glox + -9glox = 9glox + -9glox

Combine like terms: 18glox + -9glox = 9glox
-171glo + 9glox = 9glox + -9glox

Combine like terms: 9glox + -9glox = 0
-171glo + 9glox = 0

Factor out the Greatest Common Factor (GCF), '9glo'.
9glo(-19 + x) = 0

Ignore the factor 9.

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 '(-19 + x)' equal to zero and attempt to solve: Simplifying -19 + x = 0 Solving -19 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = 0 + 19 Combine like terms: -19 + 19 = 0 0 + x = 0 + 19 x = 0 + 19 Combine like terms: 0 + 19 = 19 x = 19 Add '-1x' to each side of the equation. x + -1x = 19 + -1x Combine like terms: x + -1x = 0 0 = 19 + -1x Simplifying 0 = 19 + -1x 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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