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No. The so-called "natural" logarithms have a base of ' e ', and you can find the log of any positive number to any base you like.
the base is the number you start with... like 8 squared... your base will be 8 and your square will be 2... that means 8 squared would be 8x8... = 64... hope this helps!!
It could mean the base of a number system, such as decimal is base-10, or binary is base-2, or hexidecimal is base-16. Or it can refer to when a number has an exponent, like 23, 2 is the base, and 3 is the exponent. Or ex, where e represents the base of the natural logarithm. Here is another word 'base'. This is related to the base/exponent meaning.Another meaning for base is in solid geometry, such as a cylinder has a base (the circle part).
There would need to be a digit which represents Ten. This would be the largest digit. Any number can be represented in any number-base system, so there is no 'largest number' just largest digit. Base eleven is not commonly used as some of the others (like hexadecimal, which uses letters A-F to represent ten through fifteen). You could use A for ten or maybe you want to use X (like roman numeral ten).
If you are multiplying powers of the same base (like 24 times 211), yes, you add the exponents.