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

Determine y inverse for x2 + y 4 = 10, Determine  y′′  for           ...

Determine  y′′  for                                x 2 + y 4   = 10 Solution: We know that to get the second derivative we required the first derivative and to get that w

Draw the bipartite graph, The graph C n , n  ≥  3 contains n vertices and n...

The graph C n , n  ≥  3 contains n vertices and n edges creating a cycle. For what value of n is C n a bipartite graph? Draw the bipartite graph of C n to give explanation for yo

Standard basis vectors -application of scalar multiplication, Standard Basi...

Standard Basis Vectors Revisited In the preceding section we introduced the idea of standard basis vectors with no really discussing why they were significant.  We can now do

MATLAB, program of curve revolve and create a surface

program of curve revolve and create a surface

Compute the quartile coefficient of skewness, By using the above data compu...

By using the above data compute the quartile coefficient of skewness Quartile coefficient of skewness = (Q3 + Q1 - 2Q2)/(Q3 + Q1)                                The positio

How many hours will it take before the cars are 610 miles, Two commuters le...

Two commuters leave the similar city at the same time but travel in opposite directions. One car is traveling at an average speed of 63 miles per hour, and the other car is traveli

Which number falls among 5.56 and 5.81, Which number falls among 5.56 and 5...

Which number falls among 5.56 and 5.81? If you add a zero to the end of 5.6 to get 5.60, it is simpler to see that 5.56

What did she pay per pound, Mona purchased one and a half pounds of turkey ...

Mona purchased one and a half pounds of turkey at the deli for $6.90. What did she pay per pound? Divide the cost of the turkey by the weight; $6.90 ÷ 1.5 = $4.60.

Parallel lines, Parallel to the line specified by 10 y + 3x= -2 In this...

Parallel to the line specified by 10 y + 3x= -2 In this case the new line is to be parallel to the line given by 10 y ? 3x ? -2 and so it have to have the similar slope as this

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