Question

Please walk me through this :
Given 2x-y=4 and (2^x)(2^y)=32, which of
the following represents x-y :
a. -2
b. -1
c. 0
d. 1
e. 2

Answer 1

@jdoe0001 do you know how to do this?

Answer 2

well
keep in mind that
\(\bf 2^x\times 2^y = 36\\
\color{blue}{36 = 2^5\\
a^x \times a^y = a^{x+y}}\\
\text{so the only 2 possible values lies within 5}\)

Answer 3

you lost me at 36=2^5

Answer 4

2^5 is 32

Answer 5

then we'd just have to check that those 2 values give us
2x-y = 4

so let's try a combination
4 and 1
2(4)-(1) \(\bf \ne\) 4

another combination
3 and 2
\(\bf 2(3) -(2) = 4\)

what about
2 and 3

2(2)-(3) \(\bf \ne\) 4

Answer 6

so the one that worked was 3 and 2
so y = 2, x =3, and you'd know then what x-y is :)

Answer 7

ohh .. \(\bf 2^5 = 36\)
that is
2 x 2 x 2 x 2 x 2 = 36

Answer 8

confused still?

Answer 9

acck, I meant 32, not 36 :/

Answer 10

so much for my typos :(

Answer 11

ohhhh and 3,2 has to work for the other one right: (2^x)(2^y)=32 and i checked and it does....... oh ok at the 2^5 lol
and the answer is -1?

Answer 12

I MEAN +1 SORRY TYPO

Answer 13

yes +1 :)

Answer 14

\(\bf 2^x\times 2^y = 32\\
2^x\times 2^y \implies 2^{x+y} = 2^5\\
x+y = 5\)

Answer 15

thanks, that was actually easy :)

Answer 16

yw