Log[4](2x+6)=2

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Solution for Log[4](2x+6)=2 equation:


Simplifying
Log[4](2x + 6) = 2

Reorder the terms:
goL * 4(6 + 2x) = 2

Reorder the terms for easier multiplication:
4goL(6 + 2x) = 2
(6 * 4goL + 2x * 4goL) = 2
(24goL + 8goxL) = 2

Solving
24goL + 8goxL = 2

Solving for variable 'g'.

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

Reorder the terms:
-2 + 24goL + 8goxL = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 24goL + 8goxL = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 12goL + 4goxL) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + 12goL + 4goxL)' equal to zero and attempt to solve: Simplifying -1 + 12goL + 4goxL = 0 Solving -1 + 12goL + 4goxL = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 12goL + 1 + 4goxL = 0 + 1 Reorder the terms: -1 + 1 + 12goL + 4goxL = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 12goL + 4goxL = 0 + 1 12goL + 4goxL = 0 + 1 Combine like terms: 0 + 1 = 1 12goL + 4goxL = 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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