log[9](2x-5)-log[9](7)=log[9](3)

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Solution for log[9](2x-5)-log[9](7)=log[9](3) equation:


Simplifying
log[9](2x + -5) + -1log[9](7) = log[9](3)

Reorder the terms:
glo * 9(-5 + 2x) + -1log[9](7) = log[9](3)

Reorder the terms for easier multiplication:
9glo(-5 + 2x) + -1log[9](7) = log[9](3)
(-5 * 9glo + 2x * 9glo) + -1log[9](7) = log[9](3)
(-45glo + 18glox) + -1log[9](7) = log[9](3)

Reorder the terms for easier multiplication:
-45glo + 18glox + -1 * 9 * 7glo = log[9](3)

Multiply -1 * 9
-45glo + 18glox + -9 * 7glo = log[9](3)

Multiply -9 * 7
-45glo + 18glox + -63glo = log[9](3)

Reorder the terms:
-45glo + -63glo + 18glox = log[9](3)

Combine like terms: -45glo + -63glo = -108glo
-108glo + 18glox = log[9](3)

Reorder the terms for easier multiplication:
-108glo + 18glox = 9 * 3glo

Multiply 9 * 3
-108glo + 18glox = 27glo

Solving
-108glo + 18glox = 27glo

Solving for variable 'g'.

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

Add '-27glo' to each side of the equation.
-108glo + -27glo + 18glox = 27glo + -27glo

Combine like terms: -108glo + -27glo = -135glo
-135glo + 18glox = 27glo + -27glo

Combine like terms: 27glo + -27glo = 0
-135glo + 18glox = 0

Factor out the Greatest Common Factor (GCF), '9glo'.
9glo(-15 + 2x) = 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 '(-15 + 2x)' equal to zero and attempt to solve: Simplifying -15 + 2x = 0 Solving -15 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + 2x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 2x = 0 + 15 2x = 0 + 15 Combine like terms: 0 + 15 = 15 2x = 15 Add '-2x' to each side of the equation. 2x + -2x = 15 + -2x Combine like terms: 2x + -2x = 0 0 = 15 + -2x Simplifying 0 = 15 + -2x 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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