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

Example of one-to-one correspondence, An educator placed 10 pebbles in a ro...

An educator placed 10 pebbles in a row and asked four-year-old Jaswant to count how many there were. She asked him to touch the pebbles .while counting them. Jaswant counted the pe

Geometry, the figure is a rectangle with angle y=60. Find angle x

the figure is a rectangle with angle y=60. Find angle x

Simple equations, three times the first of the three consecutive odd intege...

three times the first of the three consecutive odd integers is 3 more than twice the third integer. find the third integer.

Find the shortest weighted paths, 1. Answer the questions about the graph b...

1. Answer the questions about the graph below. a. Name one cycle that begins and ends at B. b. True/False - the graph is strongly connected.  If not, explain why not.

Continuity, give me some examples on continuity

give me some examples on continuity

Logarithmic function:solve for x: 4 log x2, Solve for x: 4 log x = log (15 ...

Solve for x: 4 log x = log (15 x 2 + 16) Solution:              x 4 - 15 x 2 - 16 = 0                (x 2 + 1)(x 2 - 16) = 0                x = ± 4   But log x is

Share and dividend, to use newspaper and report on share and dividend

to use newspaper and report on share and dividend

Nonhomogeneous systems, We now require addressing nonhomogeneous systems in...

We now require addressing nonhomogeneous systems in brief. Both of the methods which we looked at back in the second order differential equations section can also be used now.  Sin

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