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Find a formula for the number of digits of 2^n. Now the textbook answer is '1+|_n*lg2_|',...

Find a formula for the number of digits of 2^n.

Now the textbook answer is '1+|_n*lg2_|', the symbol used is integer floor, and lg2 is log(10)2.

Question: How do I find this formula?? Show me the process of finding this formula. I know that when n=3, the number of digit is 1; when n goes pass 3, there will be 2 digits; when n goes pass 6, there will be 3 digits, and so on.

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