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The logarithm of a number is another number which, if used as the exponent of a third number, yields the first number.

The third number is called the base. Usually, it is 10 (common logarithm) or e (2.71828..., natural logarithm).

As an example, the common logarithm of 100 is 2. This meets the equation...

102 = 100

... whereas the natural logarithm of 100 is about 4.61...

2.718284.61 = (about) 100

One useful function of logarithms is in the multiplication of numbers. If you want to multiply two numbers, you can either just multiply them, or you can add their logarithms together and do the inverse logarithm (power) of the result. For instance...

10 * 100 = 1000

log10 10 = 1

log10 100 = 2

1 + 2 = 3

103 = 1000

This technique is used in slide rules, and it can also be used visually, to come up with a rough estimate of the product of two numbers.

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Q: Can you explain what the function of logarithms are?
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