log[4](7)-log[4](3x)=2

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Solution for log[4](7)-log[4](3x)=2 equation:


Simplifying
log[4](7) + -1log[4](3x) = 2

Reorder the terms for easier multiplication:
4 * 7glo + -1log[4](3x) = 2

Multiply 4 * 7
28glo + -1log[4](3x) = 2

Remove parenthesis around (3x)
28glo + -1glo * 4 * 3x = 2

Reorder the terms for easier multiplication:
28glo + -1 * 4 * 3glo * x = 2

Multiply -1 * 4
28glo + -4 * 3glo * x = 2

Multiply -4 * 3
28glo + -12glo * x = 2

Multiply glo * x
28glo + -12glox = 2

Solving
28glo + -12glox = 2

Solving for variable 'g'.

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

Reorder the terms:
-2 + 28glo + -12glox = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 28glo + -12glox = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 14glo + -6glox) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + 14glo + -6glox)' equal to zero and attempt to solve: Simplifying -1 + 14glo + -6glox = 0 Solving -1 + 14glo + -6glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 14glo + 1 + -6glox = 0 + 1 Reorder the terms: -1 + 1 + 14glo + -6glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 14glo + -6glox = 0 + 1 14glo + -6glox = 0 + 1 Combine like terms: 0 + 1 = 1 14glo + -6glox = 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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