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

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Solution for log[4](x-1)+log[4](x-7)=2 equation:


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

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

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

Reorder the terms:
-4glo + 4glox + glo * 4(-7 + x) = 2

Reorder the terms for easier multiplication:
-4glo + 4glox + 4glo(-7 + x) = 2
-4glo + 4glox + (-7 * 4glo + x * 4glo) = 2
-4glo + 4glox + (-28glo + 4glox) = 2

Reorder the terms:
-4glo + -28glo + 4glox + 4glox = 2

Combine like terms: -4glo + -28glo = -32glo
-32glo + 4glox + 4glox = 2

Combine like terms: 4glox + 4glox = 8glox
-32glo + 8glox = 2

Solving
-32glo + 8glox = 2

Solving for variable 'g'.

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

Reorder the terms:
-2 + -32glo + 8glox = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -32glo + 8glox = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -16glo + 4glox) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + -16glo + 4glox)' equal to zero and attempt to solve: Simplifying -1 + -16glo + 4glox = 0 Solving -1 + -16glo + 4glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -16glo + 1 + 4glox = 0 + 1 Reorder the terms: -1 + 1 + -16glo + 4glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -16glo + 4glox = 0 + 1 -16glo + 4glox = 0 + 1 Combine like terms: 0 + 1 = 1 -16glo + 4glox = 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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