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Browse High School Logarithms

Stars indicate particularly interesting answers or good places to begin browsing

Natural Logarithms [11/15/1999]
Why are natural logarithms called "natural"?

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.

Sum Square Root Search [03/06/2015]
An adult wonders for what integer is the sum of the digits of its square equal to the square root of the number. With some programming premised on logarithmic thinking, Doctor Ali provides numerical solutions.

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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