log[4](3x+2)=log[4](2x+5)

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Solution for log[4](3x+2)=log[4](2x+5) equation:


Simplifying
log[4](3x + 2) = log[4](2x + 5)

Reorder the terms:
glo * 4(2 + 3x) = log[4](2x + 5)

Reorder the terms for easier multiplication:
4glo(2 + 3x) = log[4](2x + 5)
(2 * 4glo + 3x * 4glo) = log[4](2x + 5)
(8glo + 12glox) = log[4](2x + 5)

Reorder the terms:
8glo + 12glox = glo * 4(5 + 2x)

Reorder the terms for easier multiplication:
8glo + 12glox = 4glo(5 + 2x)
8glo + 12glox = (5 * 4glo + 2x * 4glo)
8glo + 12glox = (20glo + 8glox)

Solving
8glo + 12glox = 20glo + 8glox

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.
8glo + -20glo + 12glox = 20glo + -20glo + 8glox

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

Combine like terms: 20glo + -20glo = 0
-12glo + 12glox = 0 + 8glox
-12glo + 12glox = 8glox

Add '-8glox' to each side of the equation.
-12glo + 12glox + -8glox = 8glox + -8glox

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

Combine like terms: 8glox + -8glox = 0
-12glo + 4glox = 0

Factor out the Greatest Common Factor (GCF), '4glo'.
4glo(-3 + x) = 0

Ignore the factor 4.

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 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -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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