log(2x-3)+log(9-4x)=0

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Solution for log(2x-3)+log(9-4x)=0 equation:


Simplifying
log(2x + -3) + log(9 + -4x) = 0

Reorder the terms:
glo(-3 + 2x) + log(9 + -4x) = 0
(-3 * glo + 2x * glo) + log(9 + -4x) = 0
(-3glo + 2glox) + log(9 + -4x) = 0
-3glo + 2glox + (9 * glo + -4x * glo) = 0
-3glo + 2glox + (9glo + -4glox) = 0

Reorder the terms:
-3glo + 9glo + 2glox + -4glox = 0

Combine like terms: -3glo + 9glo = 6glo
6glo + 2glox + -4glox = 0

Combine like terms: 2glox + -4glox = -2glox
6glo + -2glox = 0

Solving
6glo + -2glox = 0

Solving for variable 'g'.

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

Factor out the Greatest Common Factor (GCF), '2glo'.
2glo(3 + -1x) = 0

Ignore the factor 2.

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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + x 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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