Evaluate the logarithms, Algebra

Example   Evaluate following logarithms.

log4 16

Solution

Now, the reality is that directly evaluating logarithms can be a very complicated process, even for those who actually understand them.  Usually it is much convenient to first convert the logarithm form into exponential form.  In that form usually we can get the answer pretty quickly.

What we are actually asking here is the following.

log4 16 = ?

As recommended above, let's convert this to exponential form.

                                   log4 16 = ?        ⇒ 4 ? = 16

Most of the people cannot evaluate the logarithm log4 16 right off the top of their head.  Though, most of the people can determine the exponent which we need on 4 to obtain 16 once we do the exponentiation.  So, since,

                                                         42  = 16

we need to have the following value of the logarithm.

                                                             log4 16 = 2

Expectantly, now you have an idea on how to evaluate logarithms & are beginning to get a grasp on the notation. There are a few more evaluations which we desire to do though, we have to introduce some special logarithms which occur on extremely regular basis. They are the common logarithm & the natural logarithm.  Following are the definitions & notations which we will be by using for these two logarithms.

common logarithm :    log x = log10 x

natural logarithm :       ln x =loge x

Thus, the common logarithm is just the log base 10, except we drop the "base 10" part of the notation.  Alike, the natural logarithm is just the log base e  along with a different notation and where e is the similar number which we illustrates in the earlier section and is defined to be

                             e = 2.718281827.

Posted Date: 4/8/2013 3:17:32 AM | Location : United States







Related Discussions:- Evaluate the logarithms, Assignment Help, Ask Question on Evaluate the logarithms, Get Answer, Expert's Help, Evaluate the logarithms Discussions

Write discussion on Evaluate the logarithms
Your posts are moderated
Related Questions
Example : determine the zeroes of following polynomials. P ( x)= 5x 5 - 20x 4 +5x3 + 50x2 - 20x - 40 = 5 (x + 1) 2 ( x - 2) 3 Solution In this the factoring has been


we are going to fence into a rectangular field & we know that for some cause we desire the field to have an enclosed area of 75 ft2. We also know that we desire the width of the fi

x=1-yto the second power

are these like terms

Solve (3x+ 1/ x + 4 ) ≥ 1. Solution The first thing that we have to do here is subtract 1 from both of sides and then get everything in a single rational expression.  (3

can any one help me with my geometry

In the last two sections of this chapter we desire to discuss solving equations & inequalities that have absolute values.  We will look at equations along with absolute value in th

The following is a double inequality.                                                                   -9 In a double inequality we are saying that both of the inequalities

#question ..