Question

Is it possible for the function f(x) - 5 x 2^x to have an output of 200?

Answer 1

The solution is possible

Explanation:

Given

`f(x) = 5 * 2^x`

Required

Is an output of 200, possible?

To know if it is possible or not, we start by substituting 200 for f(x)

`200 = 5 * 2^x`

Divide both sides by 5

`(200)/(5) = (5)/(5) * 2^x`

`(200)/(5) = 2^x`

`40 = 2^x`

`2^x =40`

Take logarithm of both sides

`log2^x =log40`

Apply law of logarithm

`xlog2 =log40`

Divide both sides by log2

`x = (log40)/(log2)`

`x = (1.6021)/(0.3010)`

`x = 5.32`

for f(x) = 200, x is approximately 5.32

Hence, the solution is possible