If there is one prayer that you should pray/sing every day and every hour, it is the LORD's prayer (Our FATHER in Heaven prayer)
It is the most powerful prayer. A pure heart, a clean mind, and a clear conscience is necessary for it.
- Samuel Dominic Chukwuemeka

For in GOD we live, and move, and have our being. - Acts 17:28

The Joy of a Teacher is the Success of his Students. - Samuel Chukwuemeka

# Calculators for Exponents and Logarithms

I greet you this day,
It is highly recommended that you review the notes and videos; and solve the examples before verifying your answers with the calculators.
I wrote the codes for some functions of the calculators using JavaScript, a client-side scripting language. Please use the latest Internet browsers.
The Wolfram Alpha widgets (many thanks to the developers) was used for other functions of the calculators.
Comments, ideas, areas of improvement, questions, and constructive criticisms are welcome. You may contact me.
If you are my student, please do not contact me here. Contact me via the school's system.
Thank you for visiting.

Samuel Dominic Chukwuemeka (SamDom For Peace) B.Eng., A.A.T, M.Ed., M.S

## Exponential/Logarithmic Expressions Calculator

For Exponential Expressions;
This calculator will:
(1.) Simplify exponential expressions.
(2.) Give the answer in terms of positive exponents as applicable.
(3.) Display the 3D (3-dimensional) plot of the solution as applicable.
(4.) Display the Contour plot of the solution as applicable.

For Logarithmic Expressions;
This calculator will:
(1.) Simplify logarithmic expressions.
(2.) Give the answer in terms of positive exponents as applicable.
(3.) Display the 3D (3-dimensional) plot of the solution as applicable.
(4.) Display the Contour plot of the solution as applicable.

(1.) Type your expression in the textbox (the bigger textbox).
(2.) Type it according to the examples I listed.
(3.) Delete the default expression in the textbox of the calculator.
(4.) Copy and paste the expression you typed, into the small textbox of the calculator.
(5.) Click the Submit button.
(6.) Check to make sure that it is the correct expression you typed.
For Exponential Expressions; you will see that expression in terms of positive exponent(s) if it has any negative exponent(s).
(7.) Review the answer (Exponential Expression).
(8.) Review the answers (Logarithmic Expressions). At least one of the answers is what you need.

• Using the Exponential/Logarithmic Expressions Calculator
• Exponential Expressions: Type: $5^3 * 5^{-3}$ as 5^3 * 5^(-3)
• Exponential Expressions: Type: $x^3 * x^{-3}$ as x^3 * x^(-3)
• Exponential Expressions: Type: $p^{-7} * x^{-4}$ as p^(-7) / p^(-4)
• Exponential Expressions: Type: $(d^3 * e^{-3} * f^{-2})^5$ as (d^3 * e^(-3) * f^(-2))^5
• Exponential Expressions: Type: $(5d^3 * e^{-3} * f^{-2})^{-5}$ as (5 * d^3 * e^(-3) * f^(-2))^(-5)
• Exponential Expressions: Type: $\left(\dfrac{a^{2}}{c^{-3}}\right)^{-2}$ as (a^2 / c^(-3))^(-2)
• Exponential Expressions: Type: $(-7x^2y^{-4})(-x^{-3}y^7)$ as (-7 * x^2 * y^(-4))(-1 * x^(-3) * y^7)
• Exponential Expressions: Type: $\dfrac{-48c^{-2}d^{-3}}{4c^{-3}d^{-1}}$ as (-48 * c^(-2) * d^(-3)) / (4 * c^(-3) * d^(-1))
• Logarithmic Expressions: Type: $\log 10$ as log_10(10)
• Logarithmic Expressions: Type: $\log_e{e}$ as log e
• Logarithmic Expressions: Type: $\ln e$ as log e
• Logarithmic Expressions: Type: $\log{100} - \log{10}$ as log_10(100) - log_10(10)
• Logarithmic Expressions: Type: $\log_e{100} - \log_e{10}$ as log(100) - log(10)

Solve

## Exponential/Logarithmic Equations Calculator

This calculator will:
(1.) Solve one-variable exponential equations.
(2.) Solve one-variable logarithmic equations.
(3.) Give the answer(s) in the simplest exact forms.
(4.) Graph the real solution(s) on a number line.
To see the answer(s) in the simplest / exact forms, click the Exact forms link.

(1.) Type your equation in the textbox (the bigger textbox).
(2.) Type it according to the examples I listed.
(3.) Delete the default expression in the textbox of the calculator.
(4.) Copy and paste the equation you typed, into the small textbox of the calculator.
(5.) Click the Submit button.
(6.) Check to make sure that it is the correct equation you typed.

• Using the Exponential/Logarithmic Equations Calculator
• Please follow the same pattern/format as specified in the Exponential/Logarithmic Expressions and include an equal sign to indicate that it is an equation.

Solve

## Exponential Models Calculator

Required:
Given: Datasets X and Y
To Write: Exponential Model of the Data
Show all steps

Optional:
Given: Value of the Independent Variable, x
To Find: Value of the Dependent Variable, y

Optional:
Given: Value of the Dependent Variable, y
To Find: Value of the Independent Variable, x

Dataset X Dataset Y

Find the value of y when:

Find the value of x when:

First: We shall assume a linear relationship between X and ln Y, rather than X and Y
So, let us find the values of ln Y and use this table instead.

Dataset X Dataset ln Y

Second: Let us find the slope and y-intercept of the linear relationship between x and ln y

Third: Let us transform the linear relationship into an exponential relationship
Please review the example in the homepage to see how it is done

For the Exponential Model:

The Exponential Function is:
$y$ = $^x$

(If no value of x is given, we assume the value of x to be zero)
When ,

(If no value of y is given, we assume the value of y to be zero)
When ,

## Logarithmic Models Calculator

Required:
Given: Datasets X and Y
To Write: Logarithmic Model of the Data
Show all steps

Optional:
Given: Value of the Independent Variable, x
To Find: Value of the Dependent Variable, y

Optional:
Given: Value of the Dependent Variable, y
To Find: Value of the Independent Variable, x

Dataset X Dataset Y

Find the value of y when:

Find the value of x when:

First: We shall assume a linear relationship between ln X and Y, rather than X and Y
So, let us find the values of ln X and use this table instead.

Dataset ln X Dataset Y

Second: Let us find the slope and y-intercept of the linear relationship between ln x and y

Third: Let us transform the linear relationship into a logarithmic relationship
Please review the example in the homepage to see how it is done

For the Logarithmic Model:

The Logarithmic Function is:
$y$ = + ln x

(If no value of x is given, we assume the value of x to be zero)
When ,

(If no value of y is given, we assume the value of y to be zero)
When ,