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What do logarithms mean in layman's terms?
Quora: What do logarithms mean in layman's terms?
Great answers already. I'll try to make this one much more simpler with no graphs and less numbers.
Before I explain logarithms, I'll give you an insight on one of the application areas where logs are used.
This is an image of the tragic earthquake that devastated much of Nepal in 2015. It occurred with a magnitude of 8 on the Richter scale.
Seismologists say an earthquake with a magnitude 2 is equivalent to 1 Ton of TNT explosion.
In this case, we have magnitude 8 on the scale. So, what do you think the equivalent number of TNT explosives would be?
If you thought the answer is 4 Tons, then you're wrong. Interestingly, a magnitude 8 earth quake is equivalent to a detonation of 1 Billion Tons of TNT.
Now, if you wonder how did I get to this number (1 Billion), it is because Richter is a logarithmic scale.
Explanation
We know, 10-8 = 2. similarly the inverse is, 8+2=10.
likewise, 10/2 = 5 and 5*2=10.
So we got inverses for all four operations.
Now, take the example of 10^3 = 10*10*10 = 1000. What is the inverse of this operation(exponentiation) ?
Do we have any way to put this the other way around?
Yes, that's the idea behind logarithms.
3 = log(10) 1000, if you now look in the log book for the number 1000, you should see 3.
In mathematics, the logarithm is the inverse operation to exponentiation.
The above example uses log with the base 10.
Here's another example with log base 5,
5^3 = 5*5*5 = 125 and the log equivalent for log(5) 125 = 3.
Going back to our discussion about earthquakes, when I said an earthquake with a magnitude 2 is equivalent to 1 Ton of TNT explosion, the calculation goes like this, 10^2=100=1Ton.
similarly, with a magnitude 8, 10^8 = 1 Billion Tons.
Hope this answers your question.
Great answers already. I'll try to make this one much more simpler with no graphs and less numbers.
Before I explain logarithms, I'll give you an insight on one of the application areas where logs are used.
This is an image of the tragic earthquake that devastated much of Nepal in 2015. It occurred with a magnitude of 8 on the Richter scale.
Seismologists say an earthquake with a magnitude 2 is equivalent to 1 Ton of TNT explosion.
In this case, we have magnitude 8 on the scale. So, what do you think the equivalent number of TNT explosives would be?
If you thought the answer is 4 Tons, then you're wrong. Interestingly, a magnitude 8 earth quake is equivalent to a detonation of 1 Billion Tons of TNT.
Now, if you wonder how did I get to this number (1 Billion), it is because Richter is a logarithmic scale.
Explanation
We know, 10-8 = 2. similarly the inverse is, 8+2=10.
likewise, 10/2 = 5 and 5*2=10.
So we got inverses for all four operations.
Now, take the example of 10^3 = 10*10*10 = 1000. What is the inverse of this operation(exponentiation) ?
Do we have any way to put this the other way around?
Yes, that's the idea behind logarithms.
3 = log(10) 1000, if you now look in the log book for the number 1000, you should see 3.
In mathematics, the logarithm is the inverse operation to exponentiation.
The above example uses log with the base 10.
Here's another example with log base 5,
5^3 = 5*5*5 = 125 and the log equivalent for log(5) 125 = 3.
Going back to our discussion about earthquakes, when I said an earthquake with a magnitude 2 is equivalent to 1 Ton of TNT explosion, the calculation goes like this, 10^2=100=1Ton.
similarly, with a magnitude 8, 10^8 = 1 Billion Tons.
Hope this answers your question.
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