Logarithms

 

 

     Logarithms are very similar to exponents because they are based from the same principles as exponents.  They are, in effect, an inverse operation to exponents.

 

     For example, if b^x = N, then x = log_b N.

  

     Like exponents, there are only a few basic rules that you need to understand in order to master logarithms:

 

     log_b (PQ) = log_b P + log_b Q : This is the product rule for logarithms.  The reason that the logs add in this way is exactly the same reason why exponents with the same base add.

 

     log_b(P/Q) = log_bP – log_bQ:  As you can see, this is also exactly like exponents.  Remember, x^-1 = 1/x, and so (P/Q) = P * Q^-1, and so just like when dividing exponents with the same base, taking a log of

 

     log_b(P)^r = r log_b P:  This is because of the nature of logarithms.  It is essentially the same as the exponent operation (a²)³. 

 

     So, Exponents and Logarithms are based of exactly the same principles.  If you can master one, then you can master both.  They are inverse operations of each other.