Question

I don't know how to find out this

Answer 1

The number log2(7) is:

(a)an integer
(b)a rational number
(c)an irrational number
(d)a prime number

Answer 2

\[\log_2(7)\]?

Answer 3

yes

Answer 4

hmmm good question
the answer is easy
the reasoning not so easy

Answer 5

it is pretty clear that it is not an integer, since
\[2^x=7\] has not integer solution for sure

Answer 6

yes ofcourse

Answer 7

it is also pretty clear that "prime" is a dumb filler answer, since if it is not an integer, it sure as heck is not a prime number

Answer 8

lol yes

Answer 9

the answer is it is "irrational" but i am not sure i can give you a good proof that 7 is not a rational power of 2

Answer 10

yes bingo

Answer 11

ok lets try a proof by contradiction
can't be too hard

Answer 12

fine

Answer 13

\[\log_2(7)=\frac{p}{q}\] is the start

Answer 14

yes

Answer 15

that makes
\[2^\frac{p}{q}=7\]

Answer 16

which makes
\[2^p=7^q\]

Answer 17

yes

Answer 18

now that seems pretty unlikely for any number of reasons
most obvious being the fundamental theorem of arithmetic

Answer 19

or the fact that \(2^p\) is even whereas \(7^q\) is odd

Answer 20

I got your point

Answer 21

or the fact that two exponential curves of above form can intersect only at (0, 1)

Answer 22

making \(p = q = 0\) which is not possible

Answer 23

yes thank you all