Hints About Logs

Date: 17 May 1995 06:01:50 -0400
From: Anonymous
Subject: Logarithms.

Dear Dr. Math,

I just received your initial message the other day.  I think
this organization is great.  Now you guys can help me out
with my homework.  Well my first question is:

Do you know any hints on how to figure out logarithms?
Possibly some secret little formulas the government's been
hiding for years.  Well anyway thanks a lot, and get back to
me quick, my test is tommorow.

Ara Donabedian
High School Student at Augsburg American High School
Augsburg, Germany

Date: 17 May 1995 11:04:46 -0400
From: Dr. Sydney
Subject: Re: Logarithms.

Dear Ara,

Hello!  I'm glad you wrote to us!  It is usually a lot easier for us to help
out with problems if you could tell us more specifically what kind of
problems or concepts are troubling you.  There are a lot of different kinds
of problems you could do with logs, so I'm not sure exactly what you are
having trouble with.  There is no government secret about logs (to the best
of my knowledge, that is, but I suppose you never really know...
Hmmmmm...).  

I guess if you can remember the basic properties of logs, you should be
fine.  The important ones are:

log  a = x     means b^x = a 
   b

log  (ac) = (log  a) + (log  c)
   b            b           b

log  (a/c) = (log  a) - (log  c)
   b             b          b

log  a^r = r log  a
   b            b

These are the main properties to keep in mind.  If you have any specific
questions, feel free to write back.  Good luck on your test!

--Sydney, "Dr. Math"
    

Date: 11/19/2001 at 00:56:52
From: Phyllis Stewart
Subject: More Log Hints


I have a few useful hints that you may want to add to your list:

1) If the base and the argument can be written as powers themselves, you 
can cancel like exponents or like bases.  In the examples below the a's 
cancel:

  log (base x^a) y^a = log (base x) y
  log (base a^x) a^y = log (base x) y

2) Exchange the argument and the base and you get reciprocals:

  log (base x) y = 1/[log (base y) x]

I give these tips to my students, as they are quite useful in some of 
the more difficult problems they encounter.

Phyllis Stewart
Naperville, IL