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Transcendental function - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

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  • 16 Questions around this concept.

Concepts Covered - 1

Transcendental function

Transcendental functions:  the functions which are not algebraic are called transcendental functions. Exponential, logarithmic, trigonometric and inverse trigonometric functions are transcendental functions.

Exponential Function: function f(x) such that \mathrm{f(x)=a^x} is known as an exponential function.

\\\mathrm{base:\;\;a>0,a\neq1}\\\mathrm{domain:x\in \mathbb{R}}\\\mathrm{range:f(x)>0}

 

Property : If ax = ay  ,then x = y

 

Logarithmic function:  function f(x) such that f\left ( x \right )= \log _{a} (x) is called logarithmic function 

\\\mathrm{base:\;\;a>0,a\neq1}\\\mathrm{domain:x>0}\\\mathrm{range:f(x)\in\mathbb{R}}
         

                    If a > 1                                                                               If 0 < a < 1

Properties of Logarithmic Function

\\\mathrm1.\;{\log_e(ab)=\log_ea+\log_eb}\\\mathrm{2.\;\log_e\left ( \frac{a}{b} \right )=\log_ea-\log_e b}\\\mathrm{3.\;\log_ea^m=m\log_ea}\\\mathrm{4.\;\log_aa=1}\\\mathrm{5.\;\log_{b^m}a=\frac{1}{m}\log_ba}\\\mathrm{6.\;\log_ba=\frac{1}{\log_ab}}\\\mathrm{7.\;\log_ba=\frac{\log_ma}{\log_mb}}\\\mathrm{8.\;a^{\log_am}=m}\\\mathrm{9.\;a^{\log_cb}=b^{\log_ca}}\\\mathrm{10.\;\log_ma=b\Rightarrow a=m^b}

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Transcendental function

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Transcendental function Current Topic

Sets, Roster and Set Builder form of Sets
Equal and Equivalent Sets
Subsets, Proper Subset, Improper Subset, Intervals
Finite set, Infinite set, Singleton set
Power set, Universal set
Union of sets, Properties of union
Intersection of Set, Properties of Intersection
Difference of set
Complement of a set, Law of Complement, Property of Complement
Cardinal number of some sets

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