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

Related to MCA, AskIf y=e^(a?sin?^(-1) x), prove that (1 – x2)yn+2 – (2n + ...

AskIf y=e^(a?sin?^(-1) x), prove that (1 – x2)yn+2 – (2n + 1)xyn+1 – (n2 + a2)yn = 0. Hence find the value of yn when x = 0. question #Minimum 100 words accepted#

Making connections with maths, MAKING CONNECTIONS :  you have read about w...

MAKING CONNECTIONS :  you have read about what the ability to think mathematically involves. In this section we shall discuss ways of developing this ability in children. As yo

What is multiplying fractions, What is Multiplying Fractions ? The rule...

What is Multiplying Fractions ? The rule for multiplying fractions is to "multiply across": Multiply the numerators to get the numerator of the answer. Multiply the den

Statistics quiz.., can someone help me with a statistics quiz?

can someone help me with a statistics quiz?

Halm''s differential equation, please i need the solution for halm''s diffe...

please i need the solution for halm''s differential equation

Two circles touching internally prove that ox:oy=oa:ob, Two circles touchin...

Two circles touching internally at O. OXY, OAB straight lines, the latter passing through the centres. Prove that OX : OY = OA : OB. Given : Two circles touching internally a

Inequalities and intervals, What inequalities and intervals are? If it is g...

What inequalities and intervals are? If it is given that a real number 'p' is not less than another real number 'q', we understand that either p should be equal to q or

Example of differential equations, y(x) = x -3/2 is a solution to 4x 2 y′...

y(x) = x -3/2 is a solution to 4x 2 y′′ + 12xy′ + 3y = 0 , y (4) = 1/8 , and y'(4) = -3/64 Solution :  As we noticed in previous illustration the function is a solution an

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