Question

The number of points awarded in each round of a game can be represented by f(x)=2^x where x represents the number of the round. What is x when f(x)=16

Answer 1

We can use systems of linear equations to solve this.

Remember: f(x) = y


`\left \{ {{y=2^x} \atop {y=16}} \right.`

Input 16 for y.


`16= x^2`
Get the square root of 16.
4 = x

The equation is f(4) = 2^4 when x is 16.

Answer 2

Answer: x=4

Explanation:

Given : The number of points awarded in each round of a game can be represented by
`f(x)=2^x` where x represents the number of the round.

If f(x) =16 , then we have

`16=2^x`

Since
`16=2*2*2*2=2^4`

`\Rightarrow\ 2^4=2^x`

Also, the property of exponents says that if two two powers of the same bases are equal then their exponents are equal.

`\Rightarrow\ 4=x\\\\\text{OR }\ x=4`