SOLUTION: Solve the following expression to find the unknown value: {{{ 16^(2-n)=(1/4)^(n+1)}}} I have been struggling on this for about an hour with no success. So far i have been att

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the following expression to find the unknown value: {{{ 16^(2-n)=(1/4)^(n+1)}}} I have been struggling on this for about an hour with no success. So far i have been att      Log On


   

Question 561856: Solve the following expression to find the unknown value:
+16%5E%282-n%29=%281%2F4%29%5E%28n%2B1%29
I have been struggling on this for about an hour with no success. So far i have been attempting to re-arrange the expression, but always hit a dead end.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
16^(2-n)=(1/4)^(n+1)
(2^4)^(2-n)=(4^-1)^(n+1)
2^(8-4n)=4^(-n-1)
2^(8-4n)=4^(-n-1)
2^(8-4n)=2^2^(-n-1)
2^(8-4n)=2^(-2n-2)
8-4n=-2n-2
2n=10
n=5
Check:
16^(2-n)=16^-3=.00024414..
(1/4)^(n+1)=.25^6=.00024414..