Anti-Logarithms

Date: 02/27/2001 at 22:46:22
From: Elisabeth
Subject: Anti-Logarithms

I've been trying to find information about anti-logarithms, but I 
only get vague explanations as to what they are, such as:

antilogarithm of a number   Mathematics. the number whose logarithm 
is the given number. The base must be specified for the antilogarithm 
to be uniquely defined.

FINDING ANTILOGARITHMS (also called Inverse Logarithm) 
Sometimes we know the logarithm (or ln) of a number and must work 
backwards to find the number itself. This is called finding the 
antilogarithm or inverse logarithm of the number. To do this using 
most simple scientific calculators, 
1.	enter the number, 
2.	press the inverse (inv) or shift button, then 
3.	press the log (or ln) button. It might also be labeled the 
    10x (or ex) button. 
 	Example 5: log x = 4.203; so, x = inverse log of 4.203 = 
15958.79147..... (too many significant figures) 
There are three significant figures in the mantissa of the log, so 
the number has 3 significant figures. The answer to the correct 
number of significant figures is 1.60 x 104. 
 	Example 6: log x = -15.3; 
so, x = inv log (-15.3) = 5.011872336... x 10-16 = 5 x 10-16 (1 
significant figure) 
Natural logarithms work in the same way: 
 	Example 7: ln x = 2.56; so, x = inv ln (2.56) = 
12.93581732... = 13 (2 sig. fig.) 

Could you please explain the concept of anti-logarithms to me, 
especially in conjunction with log-tables and logarithms? 

Thanks!

Date: 02/28/2001 at 10:45:25
From: Doctor Roy
Subject: Re: Anti-Logarithms

Hello,

Thanks for writing to Dr. Math.

An antilogarithm is simply exponentiation.  Let's see this with the 
following example:

     log(base 10) 13 = 1.11394335231.....

This means that 10^(1.11394335231....) = 13. An anti-logarithm is 
really finding powers of different numbers.  So, if you use the 
natural logarithm, whose base is Euler's number e, then you raise e to 
some power to get the anti-logarithm.

Exponentiation and logarithms are inverse functions of one another.  
So, if you had e^2 = 7.389056..... and wanted to find the inverse 
exponentiation, you could find the natural logarithm of 7.389056..... 
and you would come up with 2.  

I hope this helps, and feel free to write again.

- Doctor Roy, The Math Forum
  http://mathforum.org/dr.math/