What is a logarithm?
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To explain, I’m going to start with subtraction and division.
Subtraction is the “reverse” of addition. Addition is figuring out 3 + 5 + ___. Subtraction is figuring out 3 + ___ = 8, or __ + 5 = 8. By moving which number is left blank, you switch the question from an addition problem to a subtraction problem. If you want to rewrite them as proper subtraction problems, you get 8 – 3 = ___ and 8 – 5 = ____
In the same way, division is the “reverse” of multiplication. A multiplication problem is 3 * 5 = ___; and two division problems are 3 * ____ = 15 and ____ * 5 = 15. Again, moving which spot is left blank. To rewrite them: 15 / 3 = ____ and 15 / 5 = _____
The next “level” of arithmetic is powers or exponents. And exponential problem is 3^(5) = ____ (Sometimes written 3 ^ 5 = ___). A key thing to note here is that, unlike the previous two “reverse”s, in this case, you can’t switch the numbers: 3^5 isn’t the same as 5^3. For this reason, you need two different “reverse” functions.
Logarithms are one of the two “reverse”s. In this case, 3 ^ ___ = 243. Rewritten, this is Log3(243) = ____
The other “reverse” is roots. In this case, ___ ^ 5 = 243. Rewritten, Root5(243) = ___.
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To go back to your question, a logarithm is asking “Base raised to what power gives this number?”
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