



 
Hi Peter,Fthan I know a few powers of 2, for example 2^{2} = 4, 2^{3} = 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 2^{10} = 1,024 so 2^{20} = (2^{10})^{2} = (1024^{})^{2} is slightly larger than 1,000^{2} = 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
and from the properties of logs
Solve for x.
 


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