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Please show me the way of using formula log?

  • Maths -

    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.

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