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