How many times can I double x before reaching y?

Question

I have no clue on how to do this

eg.

say x is 3 and y is 500

how many times can i double 3 (3, 6, 12 etc.) without exceeding 500?

Answer 1

How about 2^z(3)=500, where 2^z is the expression that describes how many times You double

.

2^6 = 128

128 x 3 = 384

 

2^7 = 256

256 x 3 = 768, which is greater than 500.  

 

So, answer is you can double the number three 6 times.

Answer 2

2^z(3) ≤ 500

2^z ≤ 500/3

z ln 2 ≤ ln 500 - ln 3

z ≤ (ln 500 - ln 3) / ln 2