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Browse High School Logarithms

Stars indicate particularly interesting answers or good places to begin browsing

Evaluating Large Numbers [06/11/1998]
How do you evaluate 2^71 * 3? Can you use logarithms?

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 number?

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 10?

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 complex numbers)?

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 number?

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