If 8^x=2 and 3^(x+y)=81 then y=?

We'll write 8^x = 2^3x

We'll
re-write 8^x = 2 <=> 2^3x = 2

Since the bases are
matching, we'll get:

3x = 1

We'll
divide by 3:

x = 1/3

We'll use the
product property of
exponentials:

 3^(x+y)=3^x*3^y

We'll
substitute x by 1/3 and we'll write 81 as a power of 3:

 3^(1/3 + y)
= 3^4

Since the bases are matching, we'll
get:

1/3 + y = 4

We'll subtract 1/3, to
isolate y to the left side:

y = 4 -
1/3

y = 11/3