Back to: All Logarithm Solvers, Trainers and Word Problems
On This Page:
In a general case, such as when you are asked to compute  , you do not have much of
a choice but to use a calculator. Computing such a logarithm by
hand, with some precision, is possible, but very time consuming and
you will never be asked to do it in a school setting. The logarithms
that your textbook will ask you to compute, are all easy to compute
and can be computed with division and sign changes.
Some things to remember:
- The easiest logarithm to compute would be a logarithm where both
the base and the argument are natural numbers, such as
 or  Normally, in such examples, the argument (16 or 1,000)
will be some power of the base (2 or 10 in our examples).
So, to
compute such a log, start dividing the argument by the base, then
divide the result again and again until you get 1. Keep count of how
many times you did your division. That count is the logarithm. It's
that simple.
- If the logarithm base is in form
 , then
you should remember that it would be the same as logarithm with the base 9 instead of 1/9, except that you have to add a minus sign.
- Same applies to the argument of the logarithm, if it is in the form 1/16 (one over some denominator), you can replace it with 16 (the number in the denominator), but add a minus sign. As you remember from lesson on Negative Numbers, two minus signs cancel out. So, if you replaced both the base as well as the argument of the logarithm with their inverses, the sign stays the same. If you replaced only one thing, then the sign changes.
|