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What are logarithms?

You have already met with the inverse, or opposite operations - for example the opposite of addition is subtraction and the opposite of multiplication is division. In the same way, the opposite of exponentials are the logarithms.

If you have

and you don't know what x is, then you need to find the logarithm of y with the base a - this would look like the following equation:

Ok, let's practice a bit. You can easily find out that 2 to the power of 6 is equal to 64. You would write this down as

If, however you have this kind of equation

then, either by trying (which would, in more complex cases, take you a very long time!) or by using logarithms, you can find what that x is.

You would write this process as

and by either using your calculator, or by using logarithmic tables, you can find that the value of x is 6.

John Napier is credited with the invention of logarithms. You can see more about that here.

You can see copies of the original fronticepieces of Napier's work on Logarithms, or the work of his successor here.

Some other interesting mathematical concepts and their invention are described here.

Or just climb the mathematical three and see what fruit of knowledge you can pick up!

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