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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

Respuesta :

Piinoy
We can use systems of linear equations to solve this.

Remember: f(x) = y

[tex] \left \{ {{y=2^x} \atop {y=16}} \right. [/tex]

Input 16 for y.

[tex]16= x^2[/tex]
Get the square root of 16.
4 = x

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

Answer: x=4

Step-by-step explanation:

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

If f(x) =16 , then we have

[tex]16=2^x[/tex]

Since [tex]16=2\times2\times2\times2=2^4[/tex]

[tex]\Rightarrow\ 2^4=2^x[/tex]

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

[tex]\Rightarrow\ 4=x\\\\\text{OR }\ x=4[/tex]