Course Code: MATH21
Course Name: Calculus with Analytical Geometry II
Student ID:
Student Name:
Major:
1
, Question 1: Exponential as well as Logarithmic functions
A logarithmic function is one which can be identified as an inverse function pertaining to
exponentiation.
Considering a > 0, x > 0, as well as a is not equal to 1,
y = loga x if and only if x = ay
If the above is true then it could be deemed as:
f(x) = loga x
Logarithmic functions can be deemed to have certain properties which could enable one to
shorten the logarithms in case the input could be found in the format of value, proportion and
product which is taken to the power. Certain properties include rule of product rule, rule of
quotient, rule of power, rule pertaining to zero exponent as well as change of base rule (Dobson
& Barnett, 2018).
On the other hand a function that is exponential in nature is identified as a mathematics functions
in the form f (x) = ax. Here, a is identified as a constant and x is the variable. The constant is also
known as the base pertaining to the function and must be more than 0.
When considering the differences logarithmic functions could be deemed as the inverses
associated with functions that are exponential in nature.
Natural Logarithmic Function
The natural logarithmic function occurs considering the base, b, pertaining to logarithmic
function, y = logb x, will be substituted with e.
Natural Exponential Function
2
Course Name: Calculus with Analytical Geometry II
Student ID:
Student Name:
Major:
1
, Question 1: Exponential as well as Logarithmic functions
A logarithmic function is one which can be identified as an inverse function pertaining to
exponentiation.
Considering a > 0, x > 0, as well as a is not equal to 1,
y = loga x if and only if x = ay
If the above is true then it could be deemed as:
f(x) = loga x
Logarithmic functions can be deemed to have certain properties which could enable one to
shorten the logarithms in case the input could be found in the format of value, proportion and
product which is taken to the power. Certain properties include rule of product rule, rule of
quotient, rule of power, rule pertaining to zero exponent as well as change of base rule (Dobson
& Barnett, 2018).
On the other hand a function that is exponential in nature is identified as a mathematics functions
in the form f (x) = ax. Here, a is identified as a constant and x is the variable. The constant is also
known as the base pertaining to the function and must be more than 0.
When considering the differences logarithmic functions could be deemed as the inverses
associated with functions that are exponential in nature.
Natural Logarithmic Function
The natural logarithmic function occurs considering the base, b, pertaining to logarithmic
function, y = logb x, will be substituted with e.
Natural Exponential Function
2
