What is the point of Logarithms or Logs?

Question

Is it used to simplify problems? What kind of conclusions can be reached with logs? Please dumb it down for me.

Answer 1

Yes it is used to simplify certain kinds of problems.
It simplifies working with exponentials.

Answer 2

Think of a logarithm as a power. Here's a log expression:

log 10 x (the 10 is supposed to be the base, which is written as a subscript)

Now think of reading this expression like this:

"The power you raise 10 to to get x"

Let's say you have a log equation like this:

log 2 8 = 3 (again, the 2 is the base written as a subscript)

This can be read, " The power you raise 2 to to get 8 is 3"

Since logarithms are the inverse of exponential equations, you can actually rewrite this as:

2^3 = 8

I hope this somewhat helped clarify logs for you, there is much more to it than this, but this is a starting point! =)

Answer 3

The logarithm is a function in mathematics... a well known one... and an important one.

Let me start you out with a few Algebra problems.

6^x = 7776 (solve for the value of x)
4^x = 16^y (solve for y in terms of x)

Based on what you know from algebra, these problems are pretty much impossible. You know of no way to algebraically manipulate these expressions.

Logarithms give you the capability that you need.

Lets just say for example that:
a^b = c .... (a raised to the exponential power of b equals c)
Well, you already know from algebra that:
a = {b}√c .... (a equals the b root of c)

The above three variables hold the same relationship in each of the two expressions. One is solved for a, the other is solved for c.

But logarithms allow us to solve for b, also.
b = log_{a} c .... (b equals the logarithm [base a] of c)

Logarithms can be regarded as the third function in the set of functions that relate a, b, and c in "a^b = c" in terms of one another.

This is the magic of logarithms. The math works.

if 3² = 9 then √9 = 3... and also log_{3} 9 = 2

When you see it written "log_{b} c = a" think to yourself "what exponential value can I raise b to get c?"... or "b to what power makes c?"

This is very convenient to solving many algebra problems. In fact, it comes in especially handy in higher level maths, too.

So, what is the solution for: 6^x = 7776 ?

Problem:
6^x = 7776
Take the base 6 logarithm of each side:
log_{6} 6^x = log_{6} 7776
The log and the base on the left cancel:
x = log_{6} 7776

There... we solved for x. What is the value of x, though? We must evaluate:
x = 5

See, beforehand... in generic algebra... if you saw that 4^x = 16... you needed to do a little gues work to solve for x. This example isnt too hard. If you know your exponents well enough, you can easily tell that x = 2

You could have also attempt writing the 16 as 4 raised to another power. Also from guesswork and a little intuition, you can rewrite the expression 4^x = 16 as 4^x = 4^2. Now... you can compare exponents and see x=2.

Unfortunately, neither of these last two methods from basic algebra are very mathematical... and they are time consuming if the numbers or expression are difficult.

The logarithm is a function in mathematics... a function that takes this guess work and time consuming endeavor out of your life... it simplifies the mathematics and allows for relationships to be written soundly as a mathematical function. That could not have been done with the intuitive methods of old.

Answer 4

Logarithms are helpful for working with data that varies by many powers of ten (or whatever base you are using).

Imagine, for example, that you have one earthquake that has a strength of 10, one that has a strength of 100, and one that has a strength of 1000. If you take the log base 10 of each of these numbers, you'll get 1, 2, and 3 respectively. These numbers are easier to work with because they are in the same power of 10. This might not seem like a big deal in this example, but imagine if you had a strength that had 21 zeroes. It's a lot easier to work with the number 21 than 1,000,000,000,000,000,000,000!

And that's what logs are good for; making very large numbers more manageable by working with their exponents instead of the numbers themselves. As far as I know, some common things that are measured on logarithmic scales are earthquakes and sounds (decibels). I'm sure there are more.

Answer 5

Well logs are pretty much to do with exponents. You can use logs to find out the base, the power, or the answer. So if you want like a real life application. The Richter Scale (used to measure Earthquakes) kinda needs logs. Every increase of of 1 on the scale is 10x as powerful than before. (2 is 10x 1, 3 is 100x 1) So you can use logs to compare the magnitude of two earthquakes. Like if one earthquake was 5.3 on the scale, and another one was 2.7, how much stronger was the 5.3 one? Something like that, I'm just beginning logs myself, so yea..

Oh, btw the answer is 398.1x more powerful :P

Answer 6

They do (at least) two things for us.

They convert complicated multiplication or division to simple addition or subtraction.

Log(A times B) equals (Log A + Log B)

And so were the basis for the calculator that was used before modern computer circuits were portable, the "slide rule" that was used by engineers and scientists.

http://en.wikipedia.org/wiki/Slide_rule

They make it possible to easily represent things of enormously different size. Like the amount of acid or base in water, which can vary from 1 to 10 to the minus seventh, and is represented by a logarithm called "pH".

http://en.wikipedia.org/wiki/PH

Answer 7

To find patterns and for factors which arent base 10, like ones tens hundreds etc, log is http://en.wikipedia.org/wiki/Logarithm

If you understand exponents imagine log as the opposite!

Answer 8

logarithms are inverses of powers. For example the inverse of e^x is lnx.

Answer 9

Logs are basically kept to keep track of daily activities.

Answer 10

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