Log[4](3x-13)=2

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Solution for Log[4](3x-13)=2 equation:


Simplifying
Log[4](3x + -13) = 2

Reorder the terms:
goL * 4(-13 + 3x) = 2

Reorder the terms for easier multiplication:
4goL(-13 + 3x) = 2
(-13 * 4goL + 3x * 4goL) = 2
(-52goL + 12goxL) = 2

Solving
-52goL + 12goxL = 2

Solving for variable 'g'.

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

Reorder the terms:
-2 + -52goL + 12goxL = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -52goL + 12goxL = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -26goL + 6goxL) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + -26goL + 6goxL)' equal to zero and attempt to solve: Simplifying -1 + -26goL + 6goxL = 0 Solving -1 + -26goL + 6goxL = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -26goL + 1 + 6goxL = 0 + 1 Reorder the terms: -1 + 1 + -26goL + 6goxL = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -26goL + 6goxL = 0 + 1 -26goL + 6goxL = 0 + 1 Combine like terms: 0 + 1 = 1 -26goL + 6goxL = 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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