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Selected answers to common questions:
- Formula for Finding Mth Root [08/16/2001]
I read your article about finding square roots without using a calculator. Is there also a formula for finding cube roots, fourth roots and so on?
- Four Methods for Extracting Cube Roots [03/03/1998]
Extracting cube roots by factoring, calculator, guess and check, and
- Fractional Bases in Exponential and Logarithmic Functions [04/06/2009]
In the equation log_a(x) = a^x, can the base be a fraction? Doctor Ali
introduces a student to the Newton-Raphson Method and LambertW function.
- Fractional Exponents [03/11/1999]
I am trying to figure out the water consumption of the average goat.
- Fractional Exponents [12/07/2003]
When a number is raised to a power like 4/3 or 3/5, how is it done?
- Functionality of the Square Root [4/27/1996]
I maintain that the relation indicated by the statement: SQRT(x) = 3D y
(limited to real numbers) is a function, whereas my teacher claims it is
- Graphing y = (-2)^x [05/27/2005]
How do I graph y = (-2)^x, or any function where you have a negative
number raised to a power?
- Graph of y = (-n)^x [01/17/2005]
I am curious as to what the graph of y = (-n)^(x) would look like,
such as y = (-2)^x. My graphing calculator will not show the graph as
anything, but displays many real values in the table of values.
- Half Life of Money [04/13/2001]
What is the standard accepted formula for determining the amount of time
it takes for money to lose half of its value due to inflation? I've found
two, they are: t = t = log2/r and t = log2/log(1+r).
- History of Exponent Notation [11/03/2003]
Why is the symbol for exponents a smaller number above the base? How
did it become this? What is the history of it?
- History of the Radical Sign [04/17/1997]
Who invented the radical sign?
- History of the Word 'Exponent' [11/26/2003]
Who came up with the name 'exponent'?
- How Can a Number Raised to the Zero Power Be One? [01/23/2008]
I know that 3^7 * 3^0 is 3^(7+0) or 3^7. That means that 3^0 must have
a value of 1. But how is that possible?
- How Do Cube Roots Work? [11/04/2003]
I understand square roots but I'm not sure how to do cube roots. Can
- How Many Digits in 13^18 ? [05/15/2003]
Finding the exact number of digits in 13 raised to the 18th power,
with and without a calculator.
- i and (-1) with Multiple Powers [08/09/2001]
What is the order in which i and (-1) should be raised when using
multiple powers? Why is it possible to obtain so many different values?
- Importance of Linear Functions [02/06/2002]
What is the importance of linear functions in the real world, and how are
- Indirect Proof [02/14/1998]
Prove that sqrt(2) is an irrational number.
- Integral of Ln x [3/31/1996]
What is the integral of the natural log of x (ln x)?
- Interpreting 2^3^2 [04/26/2001]
Why is 2^3^2 interpreted as 2^(3^2) = 512 instead of (2^3)^2 = 64?
- An Introduction to Exponential Growth [10/07/2006]
What exactly is exponential growth? I see an equation in my book, but
I'm not sure what it means or how it works.
- Investigation Involving Square Root of 2 [07/09/2001]
How can you explain the fact that (665857/470832)^2 = 2?
- Is Doubling Exponential? [7/17/1995]
The amount of information storable in silicon has roughly doubled every
year. Many authors have written articles about this "exponential growth
rate." Is doubling exponential?
- (i)th Root and (i)th Power [02/13/1999]
How do you simplify x to the power of i (and 1/i), where x could be any
- Last Digits and High Exponents [09/26/1998]
Calculate the following expressions without a calculator: 3^1000 and 7^
134. In each, what is the final digit?
- Limits Approaching Infinity [02/16/2002]
Is the only way to answer them by memorizing all the general questions
you may come across?
- Limits to Paper Folding [05/09/2002]
What is the limit to the number of times that a piece of paper can
be folded, and how is it established?
- Logarithmic Equivalent of the Inverse Hybolic Cosine Function [10/28/1997]
I recently attempted a question which I think I have done wrong and I was
wondering if there were a set formula for this problem...
- Log Problem [5/5/1995]
Solve: 3(3^x)+9(3^-x) = 28.
- Logs in Different Bases [6/11/1996]
Solving equations with different base logs.
- Logs with Different Bases [11/26/1997]
How do you do an addition problem involving logs with different bases?
- Manually Calculating Logs and Exponents [12/16/2001]
Can you give me a formula to calculate base 10 logarithms and exponents?
- Modular Arithmetic and Finding a 13th Root [11/29/2004]
A discussion of a method for easily finding 13th roots based on
- More on Why n^0 = 1 [11/03/2007]
If 2^3=2*2*2, 2^2=2*2, and 2^1=2, shouldn't 2^0= __ or nothing,
meaning that 2^0=0?
- Multiplication of Powered Numbers [02/17/1999]
What is the product of two numbers with different powers, and how many
zeros are there at the end of the product?
- Multiplying Square Roots of Negative Numbers [11/25/2003]
It seems to me there are two possible ways to interpret a problem like
sqrt(-2) * sqrt(-2). One way I get 2 and the other way I get -2.
Which solution is correct? What's wrong with the other one?
- n^0 Power = 1: Defined or Proved? [04/18/2003]
I have been wondering if a^0 is DEFINED to be 1 or is PROVED to be 1.
- Negative Numbers Combined with Exponentials [03/09/2001]
Why in the order of operations is negation a multiplication done after
exponentiation, rather than as a part of the base? What about
- Negative Numbers to Powers [11/23/2001]
If u is an irrational number and x is a negative number, what is x^u? How
do I determine even whether that number is positive or negative?
- Nested Negative Exponents [8/2/1996]
How do I deal with nested negative exponents?