Exponential Function Calculator

An easy to use calculator to compute exponential functions of the form \( b^x \) to any base \( b \) is presented. Activities related to the product and quotient of like bases exponential rules described below, using the calculator, are also included.

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Basic Rules of Exponential Functions

The exponential function \( b^x \) is defined for \( b \gt 0 \) and \( b \ne 1 \)
1 - Product of Like Bases Rule
\[ b^x b^y = b^{x+y} \]
2 - Quotient of Like Bases Rule
\[ \dfrac{b^x}{b^y} = b^{x-y} \]


Use Exponential Calculator

Enter the argument \( x \) of the logarithmic function and its base \( b \) such that
\( x \gt 0 \) , \( b \gt 0 \) and \( b \ne 1 \)
The output of the calculator is the exponential function \( b^x \).
NOTE that natural base \( e \) is entered as the letter \( e \).

Argument: \( \quad x = \)
Base: \( \quad b =\)
Decimal Places Desired =

Answer


Activities Using the Exponential Calculator

Activity 1: Product and Quotient of Like Bases Rules
Chose any base \( b \) and use the calculator to find the values of   \( b^x \), \( b^y \), \( b^{x+y} \), \( b^x \cdot b^y \), \( \dfrac{b^x}{b^y} \) and \( b^{x-y} \)
a) Compare the quantites   \( b^x \cdot b^y \) and   \( b^{x+y} \) for each pair of values \( (x,y) \). These quantities are equal according to the product rule of like bases in 1) above.
b) Compare the quantites   \( \dfrac{b^x}{b^y} \) and   \( b^{x-y} \) for each pair of values \( (x,y) \). These quantities are equal according to the quotient of like bases rule in 2) above.

\( x \) 4 5 25 40 100 120 1000
\( b^x \)
\( y \) 2 4 5 10 25 60 100
\( b^y \)
\( \color{red}{b^x \cdot b^y} \)
\( \color{red}{b^{x+y}} \)
\( \color{blue}{\dfrac{b^x}{b^y}} \)
\( \color{blue}{b^{x-y}} \)



Activity 2: Negative Exponents
The negative exponent is defined as follows \[ b^{-x} = \dfrac{1}{b^x} \]
Use the calculator to calculate \( b^x \) and \( b^{-x} \) and compare the quantities \( b^{-x} \) and \( \dfrac{1}{b^x} \) which according to the definition above are equal.

\( x \) 4 5 25 40 100
\( b \) e 3 4 5 10
\( b^{x} \)
\( \dfrac{1}{b^x} \)
\( b^{-x} \)



More References and Links

exponential
Rules of Logarithm and Exponential - Questions with Solutions
change of base formula
Maths Calculators and Solvers .

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