Use the definition of f(x) is O(g(x)) to show that 2^x + 17 is (3^x).

By the definition we must find a C and k so that for all x> k
2^x + 17 < C*3^x

Leave the equation as it is and see if we can deduce what C and k must look like.
Just divide both sides by 2^x and we see that we want (it's a good idea to distinguish what we want from what we have

1+ (17/2^x)< C*3^x/2^x = C*(3/2)^x
Now if k>5 and x> k, we get that 2^x> 17, hence 1+(17/2^x) is smaller than 2 for all values of x> 5. Also, for x> k > 5 we know that C*(3/2)^x is greater than C*(3/2), so if we take C=4, we get that
C*(3/2)^x > 4*(3/2)> 2 > 1+(17/2^x) for all x> 5