the expression 2

^{10x-1}2^{10-3x}can be written as 2^{f(x)}, where f (x) is the function of x. find f (x)f(x)=

the expression 2^{10x-1}2^{10-3x} can be written as 2^{f(x)}, where f (x) is the function of x. find f (x)

f(x)=

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Paoli, PA

Lets start by looking at a simpler example using numbers:

2^{3}2^{4 }

2^{3} = 8

2^{4} = 16

8 * 16 = 128

We could also write it out instead of using exponents:

2 * 2 * 2 * 2 * 2 * 2 * 2 = 2^{7 }=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)}

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