I think the answer is 1.First, find the least common denominator, which is 6. Then, multiply the numerator and denominator by the same number to get 6 as the denominator.

is multiplied by 6 to get

.

is multiplied by 3 to get

.

is multiplied by 6 to get

. Since

is closest to

, 1 is the answer. Hope this helps!
I suppose that when you write "log^6" , you want to say log₆
Change of base formula:
loga b=logc b / logc a
log₆ 120=ln 120 / ln 6=2.67
Answer: log₆ 120=2.67
The system of equations have no solution.
Explanation:
The equations are
and 
To find the two numbers, let us solve the equations using substitution method.
From the equation
, let us determine the value of r,

Let us substitute the value of r in
, we get,

which is not possible.
This means that the system has no solution.
Define unit vectors along the x-axis and the y-axis as

respectively.
Then the vector from P to Q is

In component form, the vector PQ is (-8,5).
The magnitude of vector PQ is
√[(-8)² + 5²] = √(89) = 9.434
Answer:
The vector PQ is (-8, 5) and its magnitude is √89 (or 9.434).