# Using Logarithmic Tables

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^{p}

^{ }where 1≤m<10 and p is an integer(positive or negative whole number).

^{0}

^{}

^{0}. Which is equal to 2.

^{0}. = 1.153

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Express the given number "n" in the form of m * 10^{p} ^{ }where 1≤m<10 and p is an integer(positive or negative whole number).

For example number 2 is expressed as 2*10^{0}

log n become equal to p + log m

log 2 becomes equal to 0 + log 2

p is called the characeristic and log m is called the mantissa. Mantissa is read from the logarithmic tables.

Logarithmic tables are show three sets of columns

i) the first set of column on the extreme left contains numbers from 10 to 99.

ii) in the seocnd set there 10 columns headed by 0,1,2,...,9

iii) after this, in the third set there 9 more columns headed by 1,2,3...9. These are known as mean differences.

As 1≤m<10, the mantissa is for a number between 1 and 10. Hence the interpretation of the first set of column in the table is 1.0 to 9.9, If you add the digit in the second set one more digit is added to the number. Which mean 1.0 becomes 1.01. If we add a digit in the third column on more digit is added to the number. Which means 1.01 becomes 1.011.

Hence log 2 = 0 + 0.3010 = 0.3010

How to see its antilogarithm.

Antilogaritm tables are written from .00. If mantissa of a logarithm is .00, then antilogarithm is 1.000

Antilogarithm of .3010 is equal to 2.000

As the characteristic of the number is 0 the number is 2.0*10^{0}. Which is equal to 2.

Suppose the problem is to find 2^(1/6). It is 2 to the power (1/6).

When we take logarithms, it becomes (1/6)* log 2 which is equal to (1/6)*(0.3010) = 0.0617 (rounded)

What is antilogarithm of 0.0617 = 1.153*10^{0}. = 1.153

So the answer of 2^(1/6) is equal to 1.153.

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Study Plans and Revision Notes are created on the basis of the chapters in R.D. Sharma's Book

1. Sets

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2. Cartesian product of sets and relations

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3. Functions

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4. Binary operations

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5. Complex numbers

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6. Sequences and series

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11.Matrices

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14. Family of lines

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Ch.15 Circle

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Ch. 16. Parabola

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Ch. 17. Ellipse

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Ch. 18. Hyperbola

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19. Real Functions

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20. Limits

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21. Continuity and Differentiability

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22. Differentiation

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23. Tangents , Normals and other applications of derivatives

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25 Maximum and minimum values

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26. Indefinite integrals

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27. Definite Integration

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28. Areas of Bounded regions

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29. Differential equations

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30. VECTORS

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31. THREE DIMENSIONAL GEOMETRY

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32. Probability

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33. Trigonometric ratios, Identities and Maximum & Minimum Values of Trigonometrical Expressions

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Ch.34 properties of Triangles and circles connected with them

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Ch. 35. Trigonometrical equations

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36. Inverse Trigonometrical functions

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Ch. 37 Solution of Triangles

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Ch. 38 Heights and distances

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1. Sets

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2. Cartesian product of sets and relations

Study guide and notes

3. Functions

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4. Binary operations

Study guide and notes

5. Complex numbers

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6. Sequences and series

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7. Quadratic equations and expressions

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8. Permutations and Combinations

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9. Binomial theorem

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10. Exponential and logarithmic series

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11.Matrices

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12. Determinants

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13 Cartesian System of Rectangular Coordinates and straight lines

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14. Family of lines

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Ch.15 Circle

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Ch. 16. Parabola

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Ch. 17. Ellipse

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Ch. 18. Hyperbola

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19. Real Functions

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20. Limits

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21. Continuity and Differentiability

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22. Differentiation

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23. Tangents , Normals and other applications of derivatives

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24. Increasing and decreasing functions

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25 Maximum and minimum values

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26. Indefinite integrals

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27. Definite Integration

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28. Areas of Bounded regions

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29. Differential equations

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30. VECTORS

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31. THREE DIMENSIONAL GEOMETRY

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32. Probability

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33. Trigonometric ratios, Identities and Maximum & Minimum Values of Trigonometrical Expressions

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Ch.34 properties of Triangles and circles connected with them

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Ch. 35. Trigonometrical equations

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36. Inverse Trigonometrical functions

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Ch. 37 Solution of Triangles

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Ch. 38 Heights and distances

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