To do these without a calculator you need to remember the following.

Where, b, is called the base is any number such that  and .  The first is usually called logarithmic form and the second is usually called exponential form.  The logarithmic form is  read “y equals log base b of x”.

So, if you convert the logarithms to exponential form it’s usually fairly easy to compute these kinds of logarithms.

(a)  

(b)  

Note the difference between (a) and (b)!  The base, b, that you use on the logarithm is VERY important!  A different base will, in almost every case, yield a different answer.  You should always pay attention to the base!

(c)  

(d)  

(e)  

(f)  

There are a couple of quick notational issues to deal with first. 

The e in the natural logarithm is the same e used in Problem 2 above.  The common logarithm and the natural logarithm are the logarithms are encountered more often than any other logarithm so the get used to the special notation and special names. 

The work required to evaluate the logarithms in this set is the same as in problem in the previous problem.

(a)  

(b)  

(c)  

(d)  

(e)