pre-calc

get exerythintg in a common base. In this case base 2. Look 2=2^1, 4=2^2, 8=2^3, 2,4,8 in the same base.

So 2^(x+1)*8^(-x)=4
becomes

2^(x+1)*2^(3(-x))=2^2

take the log base 2

x+1-3x=2

-2x=1 or x=-1/2

check

2^(-1/2+1)*8^(1/2)=sqrt(2)*sqrt(8)=sqrt(2*8)=sqrt(16)=4 woiks

Rap

Thankyou very much! I understand it much better now.