Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 2008-01-05 00:10:44

ganesh
Registered: 2005-06-28
Posts: 25,914

### Logarithms and Linear Intepolation

By just remembering the log to the base 10 values of 3 numbers, the log to the base 10 value of any number can be calculated approximately!

and

Example 1 : Find the log to the base 10 value of 204.

We know,

=2.30103,

and

=1+{0.8451+0.4771}= 2.3222

hence,

would be 4/10th of the difference of the two

We get 2.309498 and the actual value is 2.309630, a difference only in the fourth place after the decimal!!!

This can be used for bigger numbers too, and for calculations which cannot be performed without the help of lograithms. The same method of approximation would apply to finding anti-logarithms too!

By knowing the base-changing rule in logarithm, the log to any base can be found of any number including logarithm to the base e, merely by knowing that

approximately and
approximately.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline