Hi Peter,Fthan

I know a few powers of 2, for example 2² = 4, 2³ = 8 and so on, but I don't know an x that gives 2^x = 1,000,000. Nevertheless I would like to have an idea of the size of x before I try to solve for it.

I do know a couple of facts. In the equation 2^x = 1,000,000 if x is a positive integer then 2^x is a power of 2 and hence not divisible by 5. But 2^x = 1,000,000 and 1,000,000 is divisible by 5. Thus x is not a positive integer.

I also know that 2¹⁰ = 1,024 so 2²⁰ = (2¹⁰)² = (1024)² is slightly larger than 1,000² = 1,000,000. Thus x is between 10 and 20, and likely much closer to 20 then 10.

To solve 2^x = 1,000,000 I would take the log of both sides to get

log(2^x) = log(1,000,000)

and from the properties of logs

x log(2) = log(1,000,000)

Solve for x.

I hope this helps,
Penny