(4-3x)log(3)=(x+5)log(4)

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Solution for (4-3x)log(3)=(x+5)log(4) equation:


Simplifying
(4 + -3x) * log(3) = (x + 5) * log(4)

Reorder the terms for easier multiplication:
3glo(4 + -3x) = (x + 5) * log(4)
(4 * 3glo + -3x * 3glo) = (x + 5) * log(4)
(12glo + -9glox) = (x + 5) * log(4)

Reorder the terms:
12glo + -9glox = (5 + x) * log(4)

Reorder the terms for easier multiplication:
12glo + -9glox = 4glo(5 + x)
12glo + -9glox = (5 * 4glo + x * 4glo)
12glo + -9glox = (20glo + 4glox)

Solving
12glo + -9glox = 20glo + 4glox

Solving for variable 'g'.

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

Add '-20glo' to each side of the equation.
12glo + -20glo + -9glox = 20glo + -20glo + 4glox

Combine like terms: 12glo + -20glo = -8glo
-8glo + -9glox = 20glo + -20glo + 4glox

Combine like terms: 20glo + -20glo = 0
-8glo + -9glox = 0 + 4glox
-8glo + -9glox = 4glox

Add '-4glox' to each side of the equation.
-8glo + -9glox + -4glox = 4glox + -4glox

Combine like terms: -9glox + -4glox = -13glox
-8glo + -13glox = 4glox + -4glox

Combine like terms: 4glox + -4glox = 0
-8glo + -13glox = 0

Factor out the Greatest Common Factor (GCF), '-1glo'.
-1glo(8 + 13x) = 0

Ignore the factor -1.

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 '(8 + 13x)' equal to zero and attempt to solve: Simplifying 8 + 13x = 0 Solving 8 + 13x = 0 Move all terms containing g to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 13x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 13x = 0 + -8 13x = 0 + -8 Combine like terms: 0 + -8 = -8 13x = -8 Add '-13x' to each side of the equation. 13x + -13x = -8 + -13x Combine like terms: 13x + -13x = 0 0 = -8 + -13x Simplifying 0 = -8 + -13x 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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