Question

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

Answer 1

Answer:

The solution is possible

Step-by-step 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

$\frac{200}{5} = \frac{5}{5} * 2^x$

$\frac{200}{5} = 2^x$

$40 = 2^x$

$2^x =40$

Take logarithm of both sides

$log2^x =log40$

Apply law of logarithm

$xlog2 =log40$

Divide both sides by log2

$x = \frac{log40}{log2}$

$x = \frac{1.6021}{0.3010}$

$x = 5.32$

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

Hence, the solution is possible