(a) Define an exponential function with positive base and state separately the three…

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

(a) Define an exponential function with positive base

a\,(\neq 1)

and state separately the three quantities usually named in the symbolic relation

a^{y}=x

. (b) Define a logarithmic function to the same base

a

and write the fundamental relationship that connects a statement of the form

a^{y}=x

with its logarithmic counterpart. (c) In each of the following, write only the name of the indicated quantity. (i) In

5^{3}=125

, what is the base? (ii) In

\log_{7}49=2

, what is the argument? (iii) In

\log_{10}x=y

, what is the value that plays the role of the exponent in the equivalent exponential form? (d) State the domain and range of (i)

y=a^{x}

and (ii)

y=\log_{a}x

where

a>0,\,a\neq1