Log[4](2x-1)+6=8

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Solution for Log[4](2x-1)+6=8 equation:


Simplifying
Log[4](2x + -1) + 6 = 8

Reorder the terms:
goL * 4(-1 + 2x) + 6 = 8

Reorder the terms for easier multiplication:
4goL(-1 + 2x) + 6 = 8
(-1 * 4goL + 2x * 4goL) + 6 = 8
(-4goL + 8goxL) + 6 = 8

Reorder the terms:
6 + -4goL + 8goxL = 8

Solving
6 + -4goL + 8goxL = 8

Solving for variable 'g'.

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

Add '-6' to each side of the equation.
6 + -4goL + -6 + 8goxL = 8 + -6

Reorder the terms:
6 + -6 + -4goL + 8goxL = 8 + -6

Combine like terms: 6 + -6 = 0
0 + -4goL + 8goxL = 8 + -6
-4goL + 8goxL = 8 + -6

Combine like terms: 8 + -6 = 2
-4goL + 8goxL = 2

Reorder the terms:
-2 + -4goL + 8goxL = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -4goL + 8goxL = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + -2goL + 4goxL)' equal to zero and attempt to solve: Simplifying -1 + -2goL + 4goxL = 0 Solving -1 + -2goL + 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 + -2goL + 1 + 4goxL = 0 + 1 Reorder the terms: -1 + 1 + -2goL + 4goxL = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2goL + 4goxL = 0 + 1 -2goL + 4goxL = 0 + 1 Combine like terms: 0 + 1 = 1 -2goL + 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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