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Browse High School Logarithms

Stars indicate particularly interesting answers or good places to begin browsing

Logarithmic Scales [01/16/2002]
Why might empirical scientific data be transformed to logarithmic data and presented on a logarithmic scale?

Logarithms [12/2/1995]
What is a logarithm?

Logarithms: History and Use [7/12/1996]
How do I explain why logarithms work to non-math-oriented people? Also, what is the history of the development of the concept of logarithm? Why is it called a "logarithm"?

Logarithms' Relation to Exponents [09/29/2001]
I understand what logs are, and their relation to Euler's constant, but I don't understand why they are what they are.

Logarithms with Unknown Bases [12/12/2001]
Provided only that, in some bases, log 2 = 0.607 and log 3 = 0.959, find a good value for log 5.

Significant Non-Zero Digits [11/27/2001]
How many significant digits are there in a number with no non-zero digits? Example: 00.000 Are there any?

Alternative Formulas for Growth and Decay [08/02/2002]
I have two formulas for growth and decay: q = q_0*e^(rt), and q = q_0*a^t. What is the difference between them?

Another Logarithm Problem [10/2/1995]
A math class asks how to convert between bases in logarithms.

Anti-Logarithms [02/27/2001]
Could you please explain the concept of anti-logarithms?

Antilogs [08/22/2001]
If log sub(a)10 = 0.250, then log sub(10)a equals ? The solution requires me to the take the base(a) antilogarithm of both sides. That would be 10 = a^0.250. Why is this the final answer?

Applications of Logarithms [04/15/1998]
How can I calculate the logarithm function on a number without a calculator? What are some of the uses of the logarithm function?

Are Properties of Logarithms Missing Something? [11/17/2005]
To solve the equation ln x^2 = -7, I can use two methods, each supported by properties of logarithms. But with one method I get two answers and with the other method I only get one answer. Is there an inconsistency in the properties of logarithms?

Base of Common Logarithms [05/23/2000]
Why is the base of common logarithms 10? Is it easier to work with, or is there a mathematical explanation?

Biology Logarithms [04/01/1999]
The Ph of an acidic pond is 5. What is the hydrogen ion concentration in moles per liter?

Briggs Logarithms [09/06/2001]
Why did Briggs raise 2 to the tenth power? Why did he extract the square root of 1.024 instead of 1024? Why did he extract the square root of 1.024 forty seven times?...

Briggs on Logarithms [08/28/2001]
I want to know how Briggs constructed logarithmic tables of common logarithms.

Calculating Any Root [10/13/1997]
I need to find an algorithm to determine any root of a number. I was told I could determine the estimated value by using Newton's Method...

Characteristic and Mantissa of a Common Logarithm [04/24/2003]
How do you find the characteristic and mantissa of a negative logarithm?

Coal Consumption [01/13/1997]
How long will coal reserves last if consumption increase at the rate of 3.1 percent per year?

Common Logarithims and Natural Logarithims [03/13/2005]
I am currently studying logarithims and I see that logarithms can take the form of ln or log. What is the difference between the two?

Comparing Very Large Numbers--Which Is Bigger? [12/01/2004]
How do you decide which large number is greater? For instance, how do you know whether 9!^(9!^9) is greater than 10^(10!^10)?

Complex Exponentiation [02/20/2015]
A teen struggles to evaluate expressions with complex numbers in their exponents. Using De Moivre's Theorem and polar coordinates, Doctors Ali and Peterson break down the method.

Composite Functions Using Logarithms [3/10/1996]
Suppose f and g are functions defined by f(x) = x+2 and g(x) = x. Find all x > -2 for which: 3^[g(x)*logbase3 f(x)] = f(x).

Converting a Base 2 Log [01/31/2002]
2147483647 is one less than what power of 2?

Converting Logs to Another Base [04/27/1998]
How can I use the logarithm function in base e to find a logarithm in base 10 or a logarithm in base n?

Converting mW to dB [06/14/2001]
I found this equation during a radio receiver discussion: 4x10-12mW = - 114dBm. How does it equate?

Decimal Exponents [03/19/1999]
Find x^y, where y is a decimal, without using a calculator.

Definition of Logarithm [04/16/2001]
In the definition of logarithm, a^x = b iff x = log_a(b) where a and b are greater than 0 and a is not equal to 1, why the stipulations? Are there any problems or contradictions that arise if they are not given?

Derivative of an Exponential Function [04/23/2007]
How can I find the derivative of an exponential function like y = 4^x?

Deriving the Change of Base Formula for Logarithms [04/13/2007]
I'm studying logs and have learned the change of base formula that says log_a(x) = log_b(x) / log_b(a). I know how to use the formula, but I don't understand why it works. Can you show me?

The Difference Between Log and Natural Log [2/8/1995]
What is the difference between log and natural log?

Division and Subtraction: Logarithm and ...? [05/30/2014]
An adult seeks insights into a proof that the logarithm satisfies f(x) - f(y) = f(x/y) for all positive x and y — and whether other functions might work, too. Doctor Vogler uses a substitution to reframe the problem before building up a proof by induction and outlining the consequences of relaxing continuity.

Does Repetitive Division Correspond to a Logarithm? [05/26/2008]
I know that logs and exponents are inverse functions. If an exponential function correlates to repeated multiplication, does a logarithmic function correlate to repeated division?

e^pi Greater Than pi^e [03/29/2003]
How can I show that e^pi is greater than pi^e without using a calculator?

Equation of Straight Line on the Log-Log Scale [03/06/2006]
I have a given graph of a straight line on a log-log axis system and need to find the equation of that line. How do I do it?

Equations with Logarithms [04/18/1997]
Find those values of 'm' for which this equation has three different solutions: x^3 - (3/2)x^2 + 5/2 = log (base 1/4) (m).

Erlang B [10/22/2002]
I need to know how to calculate the addition of numbers using logarithms: 1 + 2 + 3. There is a step that requires adding numbers that exceed Excel's limits. How can I use logs to add the numbers?

Error in One of the Laws of Logarithms? [05/02/2002]
We were discussing a problem in precalculus today and seemed to discover a basic flaw in one of the exponent laws.

Estimating Logarithms without Using a Calculator [07/28/2005]
How can I find log_4 (12) without a calculator?

Etymology of 'Logarithm' [03/19/1999]
How does the term 'logarithm' relate to the terms 'exponent' and 'knots', and to nautical logbooks?

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