Logarithmic form and exponential form, Mathematics

Assignment Help:

Logarithmic form and exponential form ; We'll begin with b = 0 , b ≠ 1. Then we have

y= logb x          is equivalent to                  x= b y

The first one is called logarithmic form and the second is called the exponential form.  Remembering this is the key to evaluating logarithms. The number b, is base.

Example Without a calculator give the precise value of following logarithms.

(a) log2 16 

 (d) log9 (1/531441) 

(e) log 1/6 36 

Solution

To rapidly evaluate logarithms the simplest thing to do is to convert the logarithm to exponential form.  Hence, let's take a look at the first one.

(a) log2 16

Firstly, let's convert to exponential form.

log2 16 =?        is equivalent to            2? = 16

Hence, we're really asking two raised to what gives 16.  As 2 raised to 4 is 16 we get,

log2 16 = 4       because            24 =16

We'll not do the remaining parts in fairly this detail, however they were all worked in this way.

 (d) log 9(1/531441) = -6        because            9-6  = 1/96  =    1 /531441

 (e) log 1/6 36   = -2      because                        (1/6)-2=62=36

Special logarithms

There are a some special logarithms that arise in many places. These are following,

Natural logarithm

                                        ln x = loge x

This log is called as the natural logarithm

Common logarithm

                                        log x = log10 x

This log is called as the common logarithm

In the natural logarithm the base e is the similar number as in the natural exponential logarithm which we saw in the last section. Given is a sketch of both of these logarithms.

2244_Logarithmic  graph.png

From this graph we get some very nice properties of the natural logarithm which we will use several times in this and later Calculus courses.

ln x → ∞                  as  x → ∞

ln x → -∞             as  x → 0, x > 0


Related Discussions:- Logarithmic form and exponential form

What is universal set, A non-empty set or group of which all the sets under...

A non-empty set or group of which all the sets under concern are subsets is known as the universal set. In any part of application of set theory, all the sets under concern might l

Disjointed sets or mutually exclusive, Disjointed Sets or Mutually Exclusiv...

Disjointed Sets or Mutually Exclusive Two sets are said to be mutually or disjointed exclusive whether they have no elements in common. Sets P and R underneath are disjointed

Partial differential equations, I need expert who can solve 10 set of PDE w...

I need expert who can solve 10 set of PDE with constant of integration.

Determine the actual viewing area, Computer monitors are calculated by thei...

Computer monitors are calculated by their diagonals. If a monitor is advertised to be 19 in, Determine the actual viewing area, considerthe screen is square? (Round to the nearest

Travel time, you are driving on a freeway to a tour that is 500 kilometers ...

you are driving on a freeway to a tour that is 500 kilometers from your home. after 30 minutes , you pass a freeway exit that you know is 50 kilometer from your home. assuming that

Formulas, how many formulas there for the (a-b)2

how many formulas there for the (a-b)2

Example of line - common polar coordinate graphs, Example of line - Common ...

Example of line - Common Polar Coordinate Graphs Example:  Graph θ = 3Π, r cos θ = 4 and r sin θ = -3 on similar axis system. Solution There actually isn't too much to

Percents, If 2/3 of a number is 24 then 1/4 of a number is...

If 2/3 of a number is 24 then 1/4 of a number is...

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