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- Exponents as Variables [11/20/2001]
I can solve these problems but I don't know how to prove them: 9^1+x= 27;
2^-x-4=1/32; 243=(1/3)^x+4; 64=0.5)^3-x.
- Finding Logarithms By Hand [04/10/1998]
How would you find a logarithm without a calculator or a table?
- Finding the Base of a Logarithm [06/08/1999]
How do I solve log (base x) 0.05 = -0.5 for x?
- 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.
- Hints About Logs [5/17/1995]
Do you know any hints on how to figure out logarithms?
- History and Applications of the Natural Logarithm [03/02/1998]
I'm so surprised at how often the number e comes up. Where did it come
from? Who first derived it? Why is it so common in the field of biology?
- How Does a Calculator Find Log? [03/23/1998]
Is there no specific formula for deriving logarithms in decimal form?
- An Identity for Solving a Logarithm Problem [1/25/1996]
I need to know the identity for solving this logarithm problem...
- Inconsistency in Complex Logarithms [06/08/2004]
I know that ln(1) = 0, but if I evaluate it as ln(-1 * -1) I find that
it equals 2pi*i, not 0. How can that be?
- Integration of Natural Logs [02/12/1998]
Why does the natural log of x equal the integral of 1/t dt from 1 to x?
Why is INT[(1/t)dt] from 1 to x the natural log of x, or why was it
defined this way?
- i Power Seen through with ln() [11/25/2010]
A student wonders about 1 raised to the square root of negative one. Starting with
natural logarithms, Doctor Ali provides some hints to evaluating this quantity raised to an imaginary exponent.
- (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
- John Napier [06/17/1998]
Why was John Napier's discovery of logarithms a great contribution to the
field of mathematics?
- Limit of a Factorial and Exponent in x [05/21/2014]
A calculus teacher wonders how to prove a limit involving the factorial of a variable raised
to a power of the same unknown. Seeing an opportunity to prove a simple version of Stirling's Approximation, Doctor Vogler introduces it with integral calculus and the Squeeze Theorem.
- Logarithm [4/6/1996]
How do you solve this question: log base 2, of 156?
- Logarithm Equation [01/22/2002]
Is there a way to solve this equation: 2x^2-1 = ln(2x^2) ?
- Logarithm Formulae [8/16/1996]
What is an algorithm or longhand procedure for calculating the logarithm
of a number?
- Logarithmic and Exponential Equations [11/28/2006]
I don't get exponential and logarithmic equations. How do logarithms
work and how do I solve equations involving exponents and logs?
- A Logarithmic Equation [08/06/1998]
How do you solve A*2^(x/y) = B for x using a base 2 logarithm?
- Logarithmic Multiplication [05/15/2003]
We found that you can rearrange bases in logarithmic multiplication.
Therefore log(b)x * log(c)y = log(c)x * log(b)y.
- Logarithmic Problem [2/22/1995]
Can you help me solve this: log 3^x = 6 + (1/2)log 9^x?
- Logarithmic Scales [12/13/1998]
Why do we use logarithmic scales and in what applications do they appear?
- Logarithm Problem [9/15/1995]
For the problem 2log(base 5) (3a+1) = log(base 5) 4 - 2log(base 5) (2a-1)
our book has an answer of 3, but we still can't figure out how they got
it; the book may be wrong but we would like to know for sure.
- Logarithm Proof [6/18/1996]
A proof involving logarithms of different bases.
- Logarithms [01/25/1998]
Why are there so many rules? How do you solve 4^x+3 = 7^x-1 ?
- Logarithms and Base E [11/20/1997]
Why is the base of a natural logarithm "e" - how did "e" receive a
value of 2.17... ?
- Logarithms before 1965 [02/08/1999]
Could you tell me how logarithms were used before the year 1965?
- Logarithms Explained and Applied [10/01/2004]
What is the number digits in the sum 2^2001 + 5^2001? It's too large
for my calculator.
- Logarithms in Bases Other Than 10 [03/28/1998]
What methods are available for solving logarithms in a base other than
- Logarithms of the Zeros of a Quadratic [03/24/2002]
If p and q are the zeros of 2x^2-mx+1=0, what is the value of log(base
2)p + log(base 2)q?
- Logarithms: Solving for T [01/30/1998]
3.5 = (1.12)^T. We can't remember how to solve for T
- 'Log' Button [01/29/1998]
We have been using the 'log' button on our calculators to solve problems
involving compound interest. What does that button do?
- The Log of a Negative Number [03/27/1998]
My calculator can't do log (-3). Is the answer a complex number?
- Log of a Negative Number [11/26/2002]
Can you explain how to find the log of a negative number (using
- Logs in Equations [05/20/1997]
How do you get rid of logs when you're trying to solve an equation?
- Logs of Complex Numbers [02/11/2004]
Give an example showing that Log(z1/z2) does not equal Log(z1) -
Log(z2) where z1 and z2 are complex numbers.
- Manually Calculating Logs and Exponents [12/16/2001]
Can you give me a formula to calculate base 10 logarithms and exponents?
- Measurements on a Logarithmic Scale [11/21/1998]
What kinds of measurements are done on a logarithmic scale? What physical
properties make a logarithmic scale more appropriate?
- Natural Logarithms [11/01/1997]
What's "natural" about natural logarithms? Why is 'e' a transcendental
- Natural Logarithms [11/15/1999]
Why are natural logarithms called "natural"?
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