>>11809912Think of it like counting digit places / orders of magnitude. It's oversimplified, but in a base 10 logarithm, 100 = 2, 1000 = 3, 10000 = 4. (That is: log10(100) = 2, meaning "log base 10 of 100 is 2").
And with binary / base 2 logarithms and numbers, 100 = 2, 1000 = 3, 10000 = 4. Same thing. You're counting the digits past the initial digit. (Just 100 in binary is "4" in base 10 / decimal.)
That's the intuitive way to think about it: how many orders of magnitude there are.
And it's the opposite of raising something to a power. (10^2 = 100, 10^3 = 1000, etc.) So you could think of logarithms as counting the powers, counting the orders of magnitude, counting the digit places, or trying to find the exponent you need to turn a base number into another number. What's the exponent you need to turn 10 into 1000? 3. So log10(1000) = 3.
