How many 2's must be multiplied together for the product to be a number between 100 and 200?
http://www.google.com/#q=2%5E7
50
To find the number of 2's that must be multiplied together for the product to be a number between 100 and 200, follow these steps:
1. Start by finding the two closest powers of 2 to the lower and upper bounds of the range. In this case, the closest power of 2 to 100 is 2^6 = 64, and the closest power of 2 to 200 is 2^7 = 128.
2. Determine how many additional 2's need to be multiplied together to reach the lower and upper bounds of the range. For the lower bound, divide 100 by 64: 100/64 = 1.5625. Since we need to round up to the next whole number, we will need 2 additional 2's. For the upper bound, divide 200 by 128: 200/128 = 1.5625. Again, rounding up, we need 2 additional 2's.
3. Finally, add up the number of additional 2's needed for the lower and upper bounds. In this case, we need 2 additional 2's for the lower bound and 2 additional 2's for the upper bound, so the total number of 2's that must be multiplied together is 2 + 2 = 4.