Logarithms Slides 614

My Introduction o

At present I am Maths Faculty at ETOOS ACADEMY

My Introduction o


o

Ex. Sr. Faculty of BANSAL CLASSES (KOTA)

My Introduction o


o

o

Ex. Sr. Faculty of BANSAL CLASSES (KOTA) IIT- Delhi

My Introduction o


o

Ex. Sr. Faculty of BANSAL CLASSES (KOTA)

o

IIT- Delhi

o

Teaching Exp. 8 Yrs.

Rank Produced by Etoos AIR-24

SURAJ SANJAY JOG And Many Others

How to Study Maths For IIT-JEE (i) Write and not read maths

How to Study Maths For IIT-JEE (i) Write and not read maths (ii) Try to apply using formulas /tricks given

How to Study Maths For IIT-JEE (i) Write and not read maths (ii) Try to apply using formulas /tricks given (iii) Practice Practice Practice

How to Make Best use of the Course Important points / formulas are highlighted

How to Make Best use of the Course Important points / formulas are highlighted Complete Assignment before moving to next lecture

Phone Number +91 9214402666


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Course Details Logrithms Trigonometry Identities (Trigo – Ph1) Quadratic Equation Sequence & Series Trigonometry Ph-2 (Trigonometry Equation)

Course Details

Solutions Of Triangle (Trigo Ph-3) Straight Lines and Pair of Straight Lines Circles Permutation & Combination

Course Details Binomial Theorem Functions ITF Limit Continuity

Course Details Derivability Method Of Derivative Indefinite Integration Definite Integration Application Of Derivatives

Course Details Vectors 3D Geometr Determinant Matrics Probability

Course Details Complex No. Differential Equation Area Under Curve Parabola Ellipse Hyperbola

Symbols ≠ < >

≤ () & … ∴ %

(not equal) ( le s s t h a n ) (greater than) (less than or equal to) u (parentheses) (and) [ellipsis (and so on)] (therefore) (percent)

Symbols π ∠ ° ⊥ ∪

(pi) (angle) (degree) (perpendicular) pa r a e ( is s im ila r t o ) (union)

∩ ∈ ∉

(intersection) (is a member of) (is not a member of)

~

Symbols ⊂ ∃ ∀ ≅ ≡ ∧ ∨

(is proper subset of) (there exists) [(for all (universal quantifier)] (is equal to or) s e qu v a e nt (and) (or)

⊆ ⊇ ⇔

(is subset of) (is super set of) (iff or implies and is implied by)

Symbols ≈

(is approxima)

∞ ! ∑ ω Γ

(infinity) (factorial) (sigma) (square root) (omega) (gamma)

θ∋ Φ

(theta) (such that) (phi)

Symbols Ω

(omega)

∆ ∏

(delta) (pi) (arrow) (derivative partial) (integral) (proportional)

→

∂ ∫ ∝ ±φ R

(plus or minus) (empty set) (set of real number)

Basic Maths Revision of Class VIII, IX, X


Remember Tables 1-19


Remember Tables 1-19 Remember Squares 1-32


Remember Tables 1-19 Remember Squares 1-32 Remember Cubes 1-12

Componendo & Dividendo

To be applied both sides of the equation

Additive Inverse,

Additive Inverse, Additive Identity,

Additive Inverse, Additive Identity, Multiplicative Inverse,

Additive Inverse, Additive Identity, Multiplicative Inverse, Multiplicative Identity

Set Theory

Classification of Sets


Roster or Tabular Form


Roster or Tabular Form

Set – Builder Form

Quadratic Equation

Inequalities

Important Algebraic Formulas a2 - b2 = (a – b) (a + b)

Important Algebraic Formulas a2 - b2 = (a – b) (a + b) (a + b)3 = a3 + b3 + 3a2b + 3ab2

Important Algebraic Formulas a2 - b2 = (a – b) (a + b) (a + b)3 = a3 + b3 + 3a2b + 3ab2 3

3

3

2

2

(a – b) = a – b + 3ab – 3a b

Important Algebraic Formulas a2 - b2 = (a – b) (a + b) (a + b)3 = a3 + b3 + 3a2b + 3ab2 3

3

3

2

2

(a – b) = a – b + 3ab – 3a b a3+b3+c3 – 3abc = (a + b + c) (Σa2 – Σab)

Number Theory

Number Theory atura

um er

Number Theory atura

um er

Whole Number (W)

Prime,

Prime, Composite,

Prime, Composite, Twin Prime,

Prime, Composite, Twin Prime, C o - P r im e

Integers (I)

Rational Numbers (Q)

Rational Numbers (Q) Converting Decimal to p/q form

Rational Numbers (Q) Converting Decimal to p/q form xamp e

Irrational Numbers

Real Numbers (R)

Complex Number (Z)

N

W

I

Q

R

Z

Exponential Form

Exponential Form

Exponential Form

Exponential Form

Logarithmic form

Logarithmic form

Loga N is defined when N > O, a > o, a

1

Logarithm Form

Logarithm Form 1.

Examples Find values :on

value

of

Logarithm

Logarithm Form 1.


value

of

Logarithm

Logarithm Form 1.


value

of

Logarithm

Logarithm Form 1.


value

of

Logarithm

Logarithm Form 1.


value

of

Logarithm

Fundamental Logarithm Identity

3 Important Deductions




Examples

Examples Find values :




Examples (Integer Type) The value of :

[JEE 2012, 4]

Examples Solve :

Examples Solve :

Antilog/Power form

Antilog/Power form

Antilog/Power form

Note It must be noted that whenever the number and the base are on the same side of unity then logarithm of that number to that base is (+ve), however if the number and the base are located on different side of unity them l o g a r it h m o f t h a t n u m b e r t o t h a t b a s e i s ( - v e )

Examples

Examples

Examples

Examples

Examples

Principal Properties of Log.




Note will not have the same .

Example 1.

Base Change Theorem

Base Change Theorem

Examples 1. If (log 23)(log34)(log45)....(logn(n+1))=10, find n


2.


2.

3. Prove that log 27 is irrational

Examples If

for permissible values of a and x then

which of the following may be correct : (A) If a rational and b rational then x can be rational.

Examples If


which of the following may be correct : (A) If a rational and b rational then x can be rational. (B)

If a irrational and b rational then x can be rational.

Examples If


which of the following may be correct : (A) If a rational and b rational then x can be rational. (B)


(C)

If a rational and b irrational then x can be rational.

Examples If


which of the following may be correct : (A) If a rational and b rational then x can be rational. (B) (C)


If a rational and b irrational then x can be rational. (D) If a and b are two irrational numbers then x can be rational.

Examples

Trichotomy True / False

For A Non Negative Number

For A Non Negative Number

‘a’ &N >2 ,n

N

Logrithmic Equations



Examples

Taking Log. Both Sides

Taking Log. Both Sides Solve for x

Taking Log. Both Sides Solve for x

Solve for x

Taking Log. Both Sides

Common and a ur a o g a r m

Characteristic & Mantissa

Examples on Characteristic & Mantissa Using log 2 = 0.3010 and log 3 = 0.4771, and log 7 = 0.8451 (A)

(B)

Examples on Characteristic & Mantissa Using log 2 = 0.3010 and log 3 = 0.4771, and log 7 = 0.8451 (A) (2)

(B)

Find the number of zeros after decimal before a significant figure start in (A)

(B)

Examples on Characteristic & Mantissa


(i) Find the number of integral and


(i) Find the number of integral and (ii) Find the largest integral value of N if


(i) Find the number of integral and (ii) Find the largest integral value of N if (iii) Find the difference of largest and smallest integral values of N if

Modulus (Absolute Value Function)

Examples on Modulus Solve for x






More Examples on Modulus Least value of x satisfying

More Examples on Modulus Least value of x satisfying

If the sum of all solutions of the equation

where b and c are relatively prime and a, b, c Find the value of (a + b + c)

N.

More Examples on Modulus







Log. Inequalities

Log. Inequalities

Log. Inequalities

Assignment Prilepko (Page No.92-93)

Examples Solve the following equations :































Solve Sheet To Attain IIT-Level

Logarithms Slides 614

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