Question

calculus I homework. please help!

Answer 1

Find y when \[2^{x}=32^{y}, 32^{x}=16^{y+1}\]

Answer 2

these are my answer choices

1. y =5/21
2. y =1/7
3. y =2/21
4. y =4/21
5. y =2/7

Answer 3

\[32=2^5\\16^{y+1}=32^x=(2^5)^x=(2^x)^5=(32^y)^5=(32)^{5y}\\so\\16^{y+1}=32^{5y}\\2^{4(y+1)}=2^{10y}\\4y+4=25y\\21y=4\\y=\frac{4}{21}\]