### Logarithms in a nutshell

Someone asked me recently to make a post about logarithms. So here goes. I already answered the person in an email but I thought I could include some interesting history tidbits here, too.

Logarithms are simply the opposite operation of exponentation.

For example, from 23 = 8 we get log28 = 3, and we read it "base 2 logarithm of 8 equals 3".

So it's not difficult: if you understand how exponents work, logarithms have the same numbers, just in a little different places.

Just as in exponentiation, a logarithm has a base (2 in the above example). Remember that in 53, 5 is called the base and 3 is the exponent.

Other examples:

53 = 125 and log5125 = 3.

104 = 10,000 and log1010,000 = 4.

2x = 345 and log2345 = x.

As you can see from the last example above, you can use logarithms to solve equations where the

4x = 1001

x = log41001.

Then you'd get the value of x from a calculator.

However, the base of the logarithm can be anything and most calculators only have two bu…

Logarithms are simply the opposite operation of exponentation.

For example, from 23 = 8 we get log28 = 3, and we read it "base 2 logarithm of 8 equals 3".

So it's not difficult: if you understand how exponents work, logarithms have the same numbers, just in a little different places.

Just as in exponentiation, a logarithm has a base (2 in the above example). Remember that in 53, 5 is called the base and 3 is the exponent.

Other examples:

53 = 125 and log5125 = 3.

104 = 10,000 and log1010,000 = 4.

2x = 345 and log2345 = x.

As you can see from the last example above, you can use logarithms to solve equations where the

*x*is the exponent:4x = 1001

x = log41001.

Then you'd get the value of x from a calculator.

However, the base of the logarithm can be anything and most calculators only have two bu…

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