SOLUTION: If 4^(x-1)=9, find the values of 2^x and 8^-x

Algebra ->  Expressions -> SOLUTION: If 4^(x-1)=9, find the values of 2^x and 8^-x      Log On


   

Question 1054651: If 4^(x-1)=9, find the values of 2^x and 8^-x
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
If 4^(x-1)=9, find the values of 2^x and 8^-x
~~~~~~~~~~~~~~~~~~~~~~~~~ 

If 4%5E%28x-1%29 = 9,  then  %281%2F4%29%2A4%5Ex = 9.


Then 4%5Ex = 36,  or  2%5E%282x%29 = 36,   or  %282%5Ex%29%5E2 = 36.


Then 2%5Ex = sqrt%2836%29  and,  hence,  2%5Ex%29 = 6.


Having this, we can write 8%5E%28-x%29 = 2%5E%28-3x%29 = %282%5Ex%29%5E%28-3%29 = 6%5E%28-3%29 = 1%2F216.

All questions are answered.