Change of base of logarithms, Mathematics

Assignment Help:

Change of base: The final topic that we have to look at in this section is the change of base formula for logarithms. The change of base formula is,

                                        log b x= loga  x / log a b

It is the most general change of base formula & will convert from base b to base a. Though ,the usual cause for using the change of base formula is to calculate the value of a logarithm that is in a base which you can't easily deal with.  By using the change of base formula means that you can write down the logarithm in terms of a logarithm which you can deal with. The two most common change of base formulas are

logb x= ln x /ln b                     and       logbx  =  log x/log b

Actually, often you will see one or the other listed as THE change of base formula!

           We can calculate the value of logarithms without the change of base formula since all the arguments could be written in terms of the base to a power. For example,

                                       log7 49 =2    because            7 2= 49

Though, this only works since 49 can be written as a power of 7! We would required the change of base formula to compute log7 50 .

log 7 50= ln 50 / ln 7= 3.91202300543/1.94591014906  = 2.0103821378

OR

log 7 50= log 50 / log 7 = 1.69897000434/0.845098040014 = 2.0103821378

Hence, it doesn't matter that we use, we will get the similar answer regardless of the logarithm which we use in the change of base formula.

Note that we could employ the change of base formula on log7 49 if we desired to as well.

                   log 7 49= ln 49/ ln 7= 3.89182029811/1.94591014906 = 2

It is a lot of work though, and is probably not the best way to deal with this.

Hence, in this section we saw how logarithms work & took a look at some properties of logarithms.  We will run into logarithms on instance so ensure that you can deal with them while we do run into them.


Related Discussions:- Change of base of logarithms

Examples on probability, 1. A machine comprises of three transformers A, B ...

1. A machine comprises of three transformers A, B and C. Such machine may operate if at least 2 transformers are working. The probability of each transformer working is given as di

Circle, Circle Well, let's recall just what a circle is. A circle is al...

Circle Well, let's recall just what a circle is. A circle is all the points which are the similar distance, r - called the radius, from a point, ( h, k ) - called the center. I

Marketing management , Draw the typical profile(s) of Shoppers'' Stop custo...

Draw the typical profile(s) of Shoppers'' Stop customers segments.

X and Y Intercepts, Find the x and y intercepts for the following equations...

Find the x and y intercepts for the following equations: 3y=3x -y=-x-4 2x+3y=6 y=5

Diferential equations, Find the normalized differential equation which has ...

Find the normalized differential equation which has {x, xex} as its fundamental set

Indicestitle.., Advantages and disadvantages of paasche indices

Advantages and disadvantages of paasche indices

Example of multiplication, Example 1: Multiply 432 by 8. Solution: ...

Example 1: Multiply 432 by 8. Solution:        432 ×        8 --------------       3,456 In multiplying the multiplier in the units column to the multiplica

Describe subtracting negative fractions, Describe Subtracting Negative Frac...

Describe Subtracting Negative Fractions? Subtracting two fractions, whether one is positive and one is negative, or whether they are both negative, is almost the same process a

Comparing, compare 643,251 633,512 and 633.893 the answer is 633.512 what i...

compare 643,251 633,512 and 633.893 the answer is 633.512 what is the question

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd