log(2x-8)-log(6x)=2

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Solution for log(2x-8)-log(6x)=2 equation:


Simplifying
log(2x + -8) + -1log(6x) = 2

Reorder the terms:
glo(-8 + 2x) + -1log(6x) = 2
(-8 * glo + 2x * glo) + -1log(6x) = 2
(-8glo + 2glox) + -1log(6x) = 2

Remove parenthesis around (6x)
-8glo + 2glox + -1glo * 6x = 2

Reorder the terms for easier multiplication:
-8glo + 2glox + -1 * 6glo * x = 2

Multiply -1 * 6
-8glo + 2glox + -6glo * x = 2

Multiply glo * x
-8glo + 2glox + -6glox = 2

Combine like terms: 2glox + -6glox = -4glox
-8glo + -4glox = 2

Solving
-8glo + -4glox = 2

Solving for variable 'g'.

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

Reorder the terms:
-2 + -8glo + -4glox = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -8glo + -4glox = 0

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

Ignore the factor -2.

Subproblem 1

Set the factor '(1 + 4glo + 2glox)' equal to zero and attempt to solve: Simplifying 1 + 4glo + 2glox = 0 Solving 1 + 4glo + 2glox = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 4glo + -1 + 2glox = 0 + -1 Reorder the terms: 1 + -1 + 4glo + 2glox = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4glo + 2glox = 0 + -1 4glo + 2glox = 0 + -1 Combine like terms: 0 + -1 = -1 4glo + 2glox = -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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