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

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


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

Remove parenthesis around (4x)
goL * 4 * 4x + log[4](x + -3) = 2

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

Multiply 4 * 4
16goL * x + log[4](x + -3) = 2

Multiply goL * x
16goxL + log[4](x + -3) = 2

Reorder the terms:
16goxL + glo * 4(-3 + x) = 2

Reorder the terms for easier multiplication:
16goxL + 4glo(-3 + x) = 2
16goxL + (-3 * 4glo + x * 4glo) = 2
16goxL + (-12glo + 4glox) = 2

Reorder the terms:
-12glo + 4glox + 16goxL = 2

Solving
-12glo + 4glox + 16goxL = 2

Solving for variable 'g'.

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

Reorder the terms:
-2 + -12glo + 4glox + 16goxL = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -12glo + 4glox + 16goxL = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -6glo + 2glox + 8goxL) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + -6glo + 2glox + 8goxL)' equal to zero and attempt to solve: Simplifying -1 + -6glo + 2glox + 8goxL = 0 Solving -1 + -6glo + 2glox + 8goxL = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -6glo + 2glox + 1 + 8goxL = 0 + 1 Reorder the terms: -1 + 1 + -6glo + 2glox + 8goxL = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6glo + 2glox + 8goxL = 0 + 1 -6glo + 2glox + 8goxL = 0 + 1 Combine like terms: 0 + 1 = 1 -6glo + 2glox + 8goxL = 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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