Does 7 appear as the leftmost digit in the decimal representation of any power of 37?
Is it possible to find a power of any counting number that has a given digit as its leftmost digit?
Also, is it possible to find a power of any counting number that begins with a given series of digits (e.g., is there a power of 24 that begins with 937)?
Prove that this is possible, or give a counter-example.
Bonus: What percentage of the powers of 2 have 1 as their leftmost digit?
Note: In finding the powers of "any counting number," exclude powers of ten, whose leftmost digit is always 1.