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December 19, 2014

December 19, 2014

Posted by **Maths** on Friday, October 14, 2011 at 4:50pm.

- Maths -
**Steve**, Saturday, October 15, 2011 at 12:39pmJust think of log as another operator, like + or * or √.

We have - to indicate the number you need to add to x to get 0:

3 + (-3) = 0

We have 1/ to indicate the number you have to multiply to get 1

x * 1/x = 1

√x is the number which you have to square to get x.

√4 = 2 --> 2² = 4

well, log(x) is the power of 10 you need to get x. The problem partly stems from the fact that we don't have a nice symbol to specify log.

log(100) = 2 because 10^2 = 100

log(0.001) = -3 because 10^-3 = 1/1000

Of course, numbers other than integer powers of 10 also have logs. Since 10^1 = 10 and 10^2 = 100, log 27 will be somewhere between 1 and 2.

In fact, log 27 = 1.43

That is, 10^1.43 = 27

So, just as by definition,

x + (-x) = 0

x * 1/x = 1

(√x)² = x

√(x²) = x

we have

log(10^x) = x

10^(log x) = x

log x is just an exponent written in an awkward way.

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