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Showing posts from March, 2020

### Logrithm formula

Formulae of Logarithm

loga mn = loga m + loga n
loga m/n = loga m - loga n
loga mn = n loga m
loga m= logb m × loga b
loge m = 2.3026 log10 m
log10 m = 0.4343 loge m

Logrithmic Series

loge ( 1+x ) = x - x2/2 + x3/3 - x4/4 +......
loge ( 1-x ) = -[x + x2/2 + x3/3 + x4/4 +......]
loge ( 1+x ) / ( 1-x ) = 2 [x + x3/3 + x5/5 +......]

### Algebra formula

Factors ( a+b )2 = a2 + b2 + 2ab ( a-b )2 = a2 + b2 - 2ab ( a2 - b2) = ( a+b ) ( a-b ) ( a2 + b2 ) = ( a+b )2- 2ab ( a+b )3 = a3 + b3 + 3ab( a+b ) ( a-b )3 = a3 - b3 - 3ab( a-b ) ( a+b+c)2 = a2 + b2 + c2 +2(ab + bc + ac ) a3 + b3 + c3 - 3 abc = ( a+b+c ) ( a2 + b2 + c2 – ab – bc – ac ) ( a+b )4 = a4 + b4 + 2ab ( 2a2 + 3ab + 2b2) ( a-b )4 = a4 + b4 - 2ab ( 2a2 + 3ab - 2b2 )
Exponential Series

ex = 1 + x/1! + x2 /2! + x3/3! + .....
e = 1 + 1/1! + 1/2! + 1/3! + ....
e = 2.7182
e-x = 1 - x/1! + x2 /2! - x3/3! + .....
ex + e-x = 2 [ 1 + x2/2! + x4/4 + .....]

Binomial Theorem

( 1+x )n = 1+nx+[n( n-1)/2!] .x2 + [n(n-1)(n-2)/3!].x3 +......
( 1+x )-n = 1-nx+[-n( n+1)/2!] .x2 - [n(n+1)(n+2)/3!].x3 +......

If x<<1
then x2,x3,.... is negligible. so:

(1+x ) -n ≈ 1-nx
(1-x ) n ≈ 1-nx
(1-x ) -n ≈ 1+nx