Question

If f(x) = a^x. and f(4) = 256 find f(5). assume a>0

Answer 1

`f(5)=1024`

Explanation:

We have the function:

`f(x)=a^x`

Where a>0.

We know that f(4)=256. Therefore:

`\displaystyle f(4)=a^4=256`

So:

`a^4=256`

Find the value of a. Take the fourth root of both sides:

`a=\sqrt[4]{256}=4`

Therefore, our function is:

`f(x)=4^x`

Hence:

`f(5)=4^5=1024`