find fx in the expression

Question

the expression 2^10x-12^10-3x can be written as 2^f(x), where f (x) is the function of x. find f (x)

f(x)= 

Answer 1

Lets start by looking at a simpler example using numbers:

 

 

 

2³2⁴ 

 

2³ = 8

2⁴ = 16

8 * 16 = 128

 

We could also write it out instead of using exponents:

 2 * 2 * 2  * 2  * 2  * 2  * 2 = 2⁷ =128

 

so we could say 2⁽³⁺⁴⁾= 2⁽⁷⁾ =  128

 

The point is, we can just add the exponents since they have the same base (2)

 

(10x-1) + (10-3x) = 7x-9

 

so f(x) = 7x-9

 

2^(7x-9)