RS Aggarwal Quantitative Aptitude PDF Free Download: LOGARITHMS

Contents [hide]



LOGARITHMS 

IMPORTANT FACTS AND FORMULAE

  1. Logarithm: If a is a positive real number, other than 1 and am = X, then we write:

          m = loga x and we say that the value of log x to the base a is m.

Example:

(i) 103 = 1000 => log10 1000 = 3

(ii) 2-3 = 1/8 => log2 1/8 = – 3

(iii) 34 = 81 => log3 81=4

(iiii) (.1)2 = .01 => log(.l) .01 = 2.

II. Properties of Logarithms:

  1. loga(xy) = loga x + loga y
  2. loga (x/y) = loga x – loga y

3.logx x=1

  1. loga 1 = 0

5.loga(xp)=p(logax)       1

  1. logax =­1/logx a
  2. logax = logb x/logb a=log x/log a.

Remember: When base is not mentioned, it is taken as 10.

  1. Common Logarithms:

         Logarithms to the base 10 are known as common logarithms.

  • The logarithm of a number contains two parts, namely characteristic and

Characteristic: The integral part of the logarithm of a number is called its characteristic.

 Case I: When the number is greater than 1.

In this case, the characteristic is one less than the number of digits in the left of the decimal point in the given number.

 Case II: When the number is less than 1.

In this case, the characteristic is one more than the number of zeros between the decimal point and the first significant digit of the number and it is negative.

Instead of – 1, – 2, etc. we write, `1 (one bar), `2 (two bar), etc.

 Example:

Number

Characteristic

Number

Characteristic

348.25

2

0.6173

`1

46.583

1

0.03125

`2

9.2193

0

0.00125

`3

Mantissa: The decimal part of the logarithm of a number is known is its mantissa. For mantissa, we look through log table.

SOLVED EXAMPLES

 1.Evaluate:

(1)log3 27

(2)log7 (1/343)

(3)log100(0.01)

SOLUTION:

  • let log3 27=3­­­­3 or n=3.

ie, log3 27 = 3.

(2)   Let log7 (1\343) = n.

Then ,7n ­=1/343

              =1/73

                    n = -3.

    ie,

     log7(1\343)= -3.

  • let log100(0.01) = n.

Then,. (100) = 0.01 = 1 /100=100 -1 0r n=-1

EX.2. evaluate

(i) log7 1=0            (ii)log34 34     (iii)36log 6 4

solution:

  1. we know that loga 1=0 ,so log7 1=0 .
  2. we know that loga a=1,so log34 34=0.

      iii)       We know that     alog 6 x =x.

                  now  36log 6 4=(62)log6   4 =6 log 6(16)=16.

Ex.3.if log  x=3 (1/3), find the value of x.

 log  x=10/3 ,x=()10/3=(23/2)10/3=2(3/2*10/3)=25=32.

Ex.4:Evaluate: (i) log53*log27 25 (ii) log 27 –log27 9

 (i)log 53 * log27 25=(log 3/log 5)*(log 25/log 27)

                            =(log 3/log 5)*(log 52*log33)

                            =(log 3/log 5)*(2log5/3log3)

                            =2/3

(ii)Let log927=n

Then,

9n =27   ó32n  =3 3    ó2n=3ó n=3/2

Again, let log279=m

Then,

27m =9   ó33m  =3 2    ó3m=2ó m=2/3

  • log927- log279=(n-m)=(3/2-2/3)=5/6

Ex 5. Simplify :(log 75/16-2 log 5/9+log 32/243)

Sol: log 75/16-2 log 5/9+log 32/243

= log 75/16-log(5/9)2+log32/243

= log 75/16-log25/81+log 32/243

= log(75/16*32/243*81/25)=log 2

Ex. 6.Find the value of x which satisfies the relation

Log10 3+log10 (4x+1)=log10 (x+1)+1

Sol: log10 3+log10 (4x+1)=log10 (x+1)+1

Log10 3+log10 (4x+1)=log10 (x+1)+log10 (x+1)+log10 10

Log10 (3(4x+1))=log10 (10(x+1))

=3(4x+1)=10(x+1)=12x+3

=10x+10

=2x=7=x=7/2

Ex. 7.Simplify:[1/logxy(xyz)+1/logyz­(xyz)+1/logzx(xyz)]

Given expression: logxyz xy+ logxyz yz+ logxyz zx

=logxyz (xy*yz*zx)=logxyz (xyz)2

  2logxyz(xyz)=2*1=2

Ex.8.If log10 2=0.30103,find the value of log10 50.

  Soln. log10 50=log10 (100/2)=log10 100-log10 2=2-0.30103=1.69897.

Ex 9.If log 2=0.3010 and log 3=0.4771,find the values of:

  1. log 25 ii)log 4.5

  Soln.

  1. log 25=log(100/4)=log 100-log 4=2-2log 2=(2-2*.3010)=1.398.
  2. log 4.5=log(9/2)=log 9-log 2=2log 3-log 2

                        =(2*0.4771-.3010)=.6532

Ex.10. If log 2=.30103,find the number of digits in 256.

    Soln.     log 256  =56log2=(56*0.30103)=16.85768.

 Its characteristics is 16.

Hence,the number of digits in 256 is 17

“Quantitative Aptitude for Competitive Examinations” by R.S. Aggarwal is a comprehensive resource widely used by aspirants preparing for various competitive exams. The book includes a dedicated chapter on Logarithms, providing detailed explanations, solved examples, and practice questions to enhance understanding of the topic.

Key Features of the Logarithms Chapter:

  • Conceptual Clarity: The chapter begins with fundamental definitions and properties of logarithms, ensuring a solid foundation.

  • Solved Examples: Numerous examples are provided to illustrate the application of logarithmic concepts in problem-solving.

  • Practice Questions: A variety of questions are included to test comprehension and improve problem-solving speed and accuracy.

Availability:

While some online platforms may offer free PDFs of this book, it’s essential to ensure that any materials you access are obtained through legal and authorized channels. Unauthorized distribution of copyrighted material is both illegal and unethical. To support the authors and publishers, and to ensure you receive accurate and up-to-date content, consider the following options:

  1. Purchase the Book:

    • You can buy the book from reputable online retailers or local bookstores. This not only ensures you have a legitimate copy but also supports the creators.
  2. Library Access:

    • Check with your institution’s library or public libraries for availability. Many libraries offer digital lending services, allowing you to access the book legally.
  3. Authorized E-Book Platforms:

    • Some platforms may offer authorized digital versions of the book for purchase or rent. Ensure that these platforms are legitimate and respect copyright laws.

Investing in the official publication not only ensures that you have the most reliable and accurate material but also supports the continued creation of quality educational resources. Remember, thorough preparation with legitimate resources is key to success in your studies and professional endeavors.

RS Aggarwal Quantitative Aptitude PDF Free Download: LOGARITHMS



error:
Contact Us

Contact Us

Contact Us

Contact Us