SOLUTION: What is the base b of the function {{{f(x)=b^x}}} if {{{f(-2)=1/64}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: What is the base b of the function {{{f(x)=b^x}}} if {{{f(-2)=1/64}}}      Log On


   

Question 130639: What is the base b of the function f%28x%29=b%5Ex if f%28-2%29=1%2F64
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=b%5Ex Start with the given function


1%2F64=b%5E%28-2%29 Plug in x=-2 and f%28-2%29=1%2F64


1%2F64=1%2Fb%5E2 Rewrite b%5E%28-2%29 as 1%2Fb%5E2


b%5E2=64 Cross multiply


b=sqrt%2864%29 Take the square root of both sides


b=8 Take the square root of 64 to get 8

So the function is f%28x%29=8%5Ex