Log 6= 0.778 ( base 10),
In other words when we multiply 10 by itself 0.778 times we get 6.
How would I multiply 10 by itself 0.778 times 🤔?
In: Mathematics
So the core of exponentials is this idea that your *growth* is proportional to your *population* or your current value.
Populations grow exponentially because each person can make multiple new people, who can go on to make multiple new people.
They don’t add in a sort of “plus plus” kind of way
They add together in a “times times” kind of way.
When you count in a “plus plus” kind of way, then 7/10 means “70% of 1”, because you are 70% over on the horizontal, and 70% up on the vertical.
But when you count in a “times times” kind of way, you don’t get that linear symmetry going on.
For example
If lillypads double in number every day
and on day 100 there are 100 lillypads
then on which day were there only 50 lillypads?
The answer is day 99
Because the next day it doubles to 100.
So now it takes some 90% of the time to get only 50% of the way, and the last 50% is covered by the last 10% of time.
This is the core of exponential growth, and logarithms are the exponential inverse of exponential growth.
So when you see that log 6 = .778
what this is telling you is that to reach 60% (out of 100%) requires 77.8% of the time (out of 100%)
Another example for the above “1” case
Log(12) of base 10
Is asking the question: “If I want to travel 120% of the distance (12 over 10), how much time will it take?”.
The calculation produces 1.08 which signifies that you traveled 120% of the distance in 108% of the time.
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