What is a logarithm?

Question

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There are some correct responses, incomplete responses, and I'll need more time to decide.

The typical algebraic procedures for fleshing-out an exponent are the functions of logarithmic operations.

It's not an inverse function of exponentiation. The value that a logarithmic operation produces: might skew your perception of values [comparing quantity]. Logarithms are algebraic "co-workers" of exponentiation.

Let's vote!

Answer 1

A logarithm is an exponent...
For example, log base 10 of 100 = 2 because 10^2 = 100.
So why do we call them logarithms? Why not just call them exponents?
Well, I've oversimplified a bit, saying a log is an exponent. Actually, it's a function which outputs the exponent of a given base. That comes in handy when you want to solve a problem that involves looking for an exponent, such as compound interest or natrual growth and decay.
All of the rules for logs come from the fact that logs are exponents. A lot of people have trouble getting used to the idea of logs, because they're inverse functions so you have to kind of "think backwards" to understand them. But once you get used to them (and that takes practice!) you'll find they make sense and youll have another item for your bag of tricks.

Answer 2

Hi,

Simply put, a logarithm is an exponent. Since 10 squared = 100, The log of 100 is 2, the exponent of the 10. The log button on calculators assumes the base number is 10, so when it says that log(24) = 1.3802, that means that 10^1.3802 = 24.

Since 2^3 = 8, then it is also true that

log__8 = 3
2 That means the log of 8 to the base 2 equals 3.
That means that the base 2 to the third power equals 8.

To find the log of 30 to the base 7 on a calculator, type in log(30)/log(7). This is the way you enter the log of a number like 30 to any base that is not the base of 10. log(30)/log(7) = 1.7479, which means that 7^1.7479 = 30.

I hope that helps.

Answer 3

It a number such that when used as an exponent of a base number produces the number it is the logarithm of. Common base numbers are 10 and e (look up e if you want)
10 to the power of 2 is 100 so the log base 10 of 100 is 2.
The advantage of logarithms before computers is that if you have a table of logarithms and look up the matching logs for big multiplication problems, you can Add the logs (insead of a big hairly multiply) and then convert the result back to number. Imagine 23456789x4302938475x50439032.
Today, logs are used because many natural things use a log basis. For example earthquakes are measured on a log scale so a 7.3 earthquake is twice as strong as a 7.0. Your hearing and judgement of loudness is related to the energy in the sound by a log.

Answer 4

I'm no expert, and it's been a long time since I learned this originally, but I'll try. Logarithms help simplify the solving of certain types of math problems, particularly those involving unknown exponents, but others too. For example, if you have to solve an equation like:
4=2^x (in English, this would read "4 equals 2 to the xth power"), the expression could be expressed in terms of logs (logarithms) which would enable you to easily single out the x and solve for its value. I think the solution is: x = log(4)/log(2) by the way. Please check http://en.wikipedia.org/wiki/Logarithm for much more info though.

Answer 5

The log of a number is the exponent to which 1 would raise the base of the log to get the original number. There are 2 commonly used bases, 10 & e. an example to make things more comprehensible:
log a=b
a=10^b for base 1o logs (also known as common or Briggsian logs)

log 100=2 since 10^2=100
log 1000=3 etc

log 3.1622776601683793319988935444327=.5 since
√10=3.1622776601683793319988935444327

logs have many useful properties such as:
log a + log b=log (ab)
log a - log b=log (a/b)
log a^b=b*log a

Answer 6

An exponent used in mathematical equations to express the level of a variable quantity (or, the power to which a number must be raised to produce a specific result).

The inverse of exponentiation; for example, a log ax = x.

Answer 7

The logarithm is the mathematical operation that is the inverse of exponentiation (raising a constant, the base, to a power).

Answer 8

A logarithm is an exponent simply put. Suppose you have this log:
log (base10) 1000
To find the answer, ask yourself: 10 to what power = 1000? 10 ^ 3 = 1000, so log (base10) 1000 = 3
Another example:
log (base 3) 9
So you ask yourself, 3 to what power = 9? The answer is 2, because 3^2 = 9.
To summarize,
log (base) number To find the answer, you ask yourself: the base to what number equals the number you are taking the log of?
base ^ x = number

Answer 9

The logarithm is the mathematical operation that is the inverse of exponentiation (raising a constant, the base, to a power).

Answer 10

The inverse of an exponential function