Logarithms

First of all sorry for posting my new post after so many days.
Today we will discuss some concepts on Logs or more properly known as Logarithims. Although many books (I do not want to write their names) says that logs are not of more importance when an exam like CAT is concerned. If you look towards the concepts involved in the topic and efforts reqired to put are less compared to other topics like Time, work and speed or say most time consuming Number systems. As i observe, when you flip through previos papers, you can surely say there will on an average 1-2 questions on Logs. But why should one spend one's time just for 2 question?? Are you asking this to yourself? I think every question is a diffrentiater of you from the entire mass.
It took 1 and a hlaf day for me to study logs. When i say 1 and half day that means the time i get after my working hours, which merely comes as 2-3 hrs at max a day. So you can gauge that it will take hardly a day for a non working person to study logs.
Well, enough of writing other things, lets get into the business right away !

When you say log, the first equation should come in front of one's eyes is : a^x = N
Which means that, X is a logarithim of N to the base a, so our equation becomes : x = log(a)N
PS : Plz note bracketed term here is the base of a log, so equation above should read as log N to the base a

Well, there are no as such more theory to discuss out here but i will put forth some key points that i feel are extremely important.

1) Log(a)b = log(c) b/ log (c) a
This means when ever you have given a problem like solve log(2)225 + log (4) 200, when
log(2) = 0.3217
Then your problem reduces as follows :
log(2)225 + log(2) 200 / log (2) 4
Now you can work on the problem as base for both of the terms are same. You can divide
log(2) 200 by log(2)4 whic hgives you log(2)50.

2) Second most important formula is : log(a)b = 1/log(b) a
This is also called as base change formula.

3) When you have equation like log(10) X = 2.abcd, then possible values for X are :
10 ^ (2+1) - 10 ^ 2
To generalize, N ^ (a+1) - N ^a
where,
N = base
a = integer part of a log or characteristic of a log, which is 2 in case of above example. (The decimal part is called as mantissa)

4) log(a) b = log(c) d
If, a= =c then b = = d
If, b = = d then a = = c

5) Log of any term to the same base is always 1, that means
log(a)a = 1

For now, these concepts are enough. I will discuss more concepts in second part of this blog.
Cheers..

Regards,
Ameya