Here I will discuss on the mental computation with maths operation like the indices and logarithm, that we may come also in some daily situations.

Below site an example. Read and enjoy it.

Example: 10

^{x}= 8

To solve this example, we need to convert it into the logarithm form to move forward.

log 10

^{x}= log 8 ---(A)

Applying the

**Laws of Logarithm**, log Y

^{x}==> x log Y

Expression (A) above, become x (1) = x = log 8

However, we are stuck here! What is the answer for log 8? And mentally?

How to carry on with mental logarithm computation?

Mental logarithm computation can be easily processed if we can simply memorise a few number of the basic logarithm.

The basic numbers that we need to remember and suffice for common mental logarithm usage are:

- log 2 = 0.301
- log 3 = 0.477
- log 7 = 0.845

With the 3 basic logarithm numbers known, we can list out the first few log to see its usefulness:

- log 1 = 0
**log 2**= 0.301**log 3**= 0.477- log 4 = log (2 x 2) =
**log 2**+**log 2**= 0.301 + 0.301 = 0.602 - log 5 = log (10 / 2) = log 10 -
**log 2**= 1 - 0.301 = 0.699 - log 6 = log (2 x 3) = log 2 +
**log 3**= 0.301 + 0.477 = 0.778 - log 7 = 0.845
- log 8 = log (2 x 2 x 2) =
**log 2**+ log 2 + log 2 = 0.301 x 3 = 0.903 - log 9 = log (3 x 3) =
**log 3**+ log 3 = 0.477 + 0.477 = 0.954 - log 10 = 1

With the above list, most of the logarithm numbers can be easily computed mentally.

But do note, however, that logarithm of

**prime**number

*cannot be done*using above method.

Examples are log 11, log 17, etc.

However, we should not be deterred from this as they are the minority and the list above serves to cover most of the logarithm solutions which can be easily done mentally.

:)

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