2log(2x+1)-2=-2log(3x-4)

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Solution for 2log(2x+1)-2=-2log(3x-4) equation:


Simplifying
2log(2x + 1) + -2 = -2log(3x + -4)

Reorder the terms:
2glo(1 + 2x) + -2 = -2log(3x + -4)
(1 * 2glo + 2x * 2glo) + -2 = -2log(3x + -4)
(2glo + 4glox) + -2 = -2log(3x + -4)

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

Reorder the terms:
-2 + 2glo + 4glox = -2glo(-4 + 3x)
-2 + 2glo + 4glox = (-4 * -2glo + 3x * -2glo)
-2 + 2glo + 4glox = (8glo + -6glox)

Solving
-2 + 2glo + 4glox = 8glo + -6glox

Solving for variable 'g'.

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

Add '-8glo' to each side of the equation.
-2 + 2glo + -8glo + 4glox = 8glo + -8glo + -6glox

Combine like terms: 2glo + -8glo = -6glo
-2 + -6glo + 4glox = 8glo + -8glo + -6glox

Combine like terms: 8glo + -8glo = 0
-2 + -6glo + 4glox = 0 + -6glox
-2 + -6glo + 4glox = -6glox

Add '6glox' to each side of the equation.
-2 + -6glo + 4glox + 6glox = -6glox + 6glox

Combine like terms: 4glox + 6glox = 10glox
-2 + -6glo + 10glox = -6glox + 6glox

Combine like terms: -6glox + 6glox = 0
-2 + -6glo + 10glox = 0

Add '2' to each side of the equation.
-2 + -6glo + 2 + 10glox = 0 + 2

Reorder the terms:
-2 + 2 + -6glo + 10glox = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -6glo + 10glox = 0 + 2
-6glo + 10glox = 0 + 2

Combine like terms: 0 + 2 = 2
-6glo + 10glox = 2

Reorder the terms:
-2 + -6glo + 10glox = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -6glo + 10glox = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -3glo + 5glox) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + -3glo + 5glox)' equal to zero and attempt to solve: Simplifying -1 + -3glo + 5glox = 0 Solving -1 + -3glo + 5glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -3glo + 1 + 5glox = 0 + 1 Reorder the terms: -1 + 1 + -3glo + 5glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3glo + 5glox = 0 + 1 -3glo + 5glox = 0 + 1 Combine like terms: 0 + 1 = 1 -3glo + 5glox = 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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