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Browse High School Logarithms

Stars indicate particularly interesting answers or good places to begin browsing

Natural Logs [12/20/1997]
I need to understand natural logs. Could you please explain them in the simplest terms possible?

n Factorial - Prove Lower Bound is n^(n/2) [09/11/2001]
I am trying to prove the following: n^(n/2) <= n!

No Logarithm of a Negative Number [8/6/1996]
log(-5) = ?

Origin of the Term Logarithm [10/27/1999]
Where does the term logarithm come from?

Perfect Logarithms [06/24/2002]
What can you tell me about the equation log(abc)= log(a+b+c)?

Population Growth Rate [9/5/1996]
If a population increases from 10 million to 300 million in 10,000 years, what is the annual growth rate?

Population of China [05/13/1997]
If the population growth rate of China is 4.3 percent and the current population of the country is 1.27 billion people, when will the population reach 2 billion?

Proof by Contradiction [05/09/2003]
Show that the log_2(7)/log_2(6) is irrational.

Radioactive Decay [10/26/2004]
The half-life of a radioactive element is 131 days, but your sample will not be useful to you after 90% of the radioactive nuclei originally present have disintegrated. For about how many days can you use the sample?

Repeated Square Roots and Logarithms [04/05/2005]
A discussion based on a calculator trick where taking 'n' repeated square roots of 'a', then subtracting 1 and multiplying by 'b', then adding 1 and squaring 'n' times, leads to a result very close to a^b. The explanation is closely related to logarithms.

Resolving Decimal Exponents [03/26/2001]
How can you find 7^.3 or 5^.6 without using a calculator? Is there more than one way of doing this?

Richter magnitude problem [11/23/1994]
The Richter magnitude, R, of an earthquake is given by R=0.67 log(0.37E)+1.46 where E is the energy in kW*h released by the earthquake. Show that if R increases by 1 unit, E increases by a factor of about 31.

Roughing It More Rigorously [12/02/2010]
A physics student wants to make sense of the various symbols used to represent "approximately equal to" -- as well as the phrase's mathematical meaning. Doctor Vogler produces two precise definitions while acknowledging that context, and personal preference, rule the day.

Seventy-two and 115: What Do Logs Have to Do with Doubling and Tripling Your Money? [02/19/2010]
Doctor Carter uses logarithms and the Taylor series to show where the 72 in the "law of 72" comes from -- and shows how the same interest rate calculations yield 115/I as an approximation for the number of years it takes an investment that bears I interest rate to triple in value.

Slide Rules [03/13/1999]
Can you help me learn how to use a slide rule?

Solving a Decibel Noise Equation [05/23/2000]
How do you rearrange the formula 50 = 94.5 - 20log(r) - 8 to solve for r?

Solving a Logarithm Equation by Substitution [12/18/2007]
I'm learning about logs, and had to solve (x+1)^(log(x+1)) = 100(x+1). My answers don't check. Can you show me where I went wrong?

Solving Logarithm Equations [04/29/2001]
How can I solve the equation: log_7(x) / log_7(4) - log_7(y) = 1, for y?

Solving Logarithms with the Quotient Rule [11/11/1998]
Can you help me solve this logarithm problem for x? I think you need to use the quotient law.

Solving Log Equation [04/20/2008]
Given log(x) + log(x + log(x)) + log(x + log(x) + log[x + log(x)]) = 0, how can I solve for x?

Solving Logistic Equations for a Variable in the Exponent [05/03/1998]
Using natural logarithms to solve for the time variable in two logisitic growth equations.

The Symbol for Natural Log [06/28/2000]
Why is "ln" and not "nl" the abbreviation for natural log?

Taking the Logarithm of Zero [08/11/2004]
Why is log(0) undefined?

Uses of Logarithms [07/20/2002]
Who uses logarithms, and for what?

Using a Rule of Logarithms [9/13/1995]
I can't figure out this problem. Can you help? log(sub)2 3k+log(sub)2 5=log(sub)2 45.

Using Logarithms to Find Number of Digits in Large Numbers [06/25/2007]
How many digits are there in 8^1000? What power of 8 has 1000 digits? What number to the 1000th power has 500 digits?

What Does x Equal? [01/16/1998]
32 * 4^2x = 12. What is x? What is a logarithm?

Why Do We Learn Logarithms? [02/28/2005]
I am currently studying logarithms in school and I was wondering what the point of them is. Will we ever use them when we grow up, and how are they used in real life?

Why Use a Logarithmic Scale to Display Data? [01/26/2008]
I read that log scales help you see data when you are looking at values that range largely. I also read that if the ear did not hear logarithmically we would only hear very loud sounds. Can you help me understand these two statements?

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