can u explain what is log?pls..... requesting?

Question

we did not get this concept till now.im 8th grade

Answer 1

A log is simply a power, or exponent, to which a number is raised to produce another number. The words log, power and exponent are all interchangeable. Essentially, they represent the number of times a given number, called the base, is used as a factor to produce the other number.

Don't let the use of the word 'log' confuse you. When used in a general discussion of powers and exponents, it is used to denote any base we may care to use. Generally however, when actually working problems from a math book, when you see something like log 3500 = x, it is talking about base 10 logarithms, unless it specifically says otherwise.

Here are some examples:

2^7 = 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128

So log(base 2) 128 = 7, because 2 is used as a factor 7 times to produce 128.

10^3 = 10 x 10 x 10 = 1000.

The base above was 10. The power, or log, was 3, because we used 10 as a factor 3 times to produce the number 1000. Using the shorthand of mathematics, if we were to take the log of 1000, base 10, we would write it like this:

log 1000 = 3

The notation 'log' was used here because we were speaking of numbers which are powers of 10. However, we could just as easily use other base systems, as in the first example above, and we often do when working math problems. A common one is 'e,' the base of the natural logarithmic system. 'e' is approximately equal to 2.718.... I added the ellipses, or dots, after the number, because 'e' is what's called an irrational number, a number whose exact value cannot be expressed as the ratio of two integers. Using mathematical shorthand, we write:

ln x = y,

where ln denotes that we are talking about the base 'e,' x represents the number resulting when 'e' is used as a factor y times. So, for example, ln e^4 = 4, because we use 'e' as a factor 4 times to get the number e^4. We can substitute 'e's approximate numerical value to obtain this:

e^4 = 2.718 x 2.718 x 2.718 x 2.718 = 54.58 (approximately).

Mathematically, we could write this:

ln e^4 = ln 54.58 = 4

Be forwarned that logs can become very complex. In fact, there are even fractional logs and logs containing variables. Here's an example of a fractional exponent:

log 31.623 = 3/2, because the square root (indicated by the bottom number, 2) of 10^3 = 1000, is 31.623 (approximately). Fractional exponents, or logs, are derived from what are called the 'laws of exponents.' But you will encounter those in later years of the study of mathematics as you continue on in your schooling. For now it is sufficient to learn the basics. After all, one must learn how to walk before learning how to run.

Answer 2

Personally, I think the logarithm is the single most difficult concept in mathematics. It's basically a way to transform an exponential function into an easier math function, like addition or multiplication.

You want to take something like Aⁿ = x and make it easier to work with. So, we use a base of A to transform it. Take the log, base A of both sides:

log(A) [Aⁿ] = log(A) [x]
n = log(A) [x]
Hopefully the log(A) [x] is a known amount, and we can then find what n is easily.

I hope that helps, but you're probably still confused. I know I was for a long time, and still have to stop & slow down and just go back to looking at and applying the formulas.

Answer 3

And adding to the catarthur's answer.. the power of log is in the fact that it makes multiplication/division terms into additive/subtractive ones, simply because of the way it is defined.

X*Y = (10^x1) * (10^y1) = 10^(x1+y1)

X/Y = (10^x1) / (10^y1) = 10^(x1-y1)

Of course, the same argument can be extended for any base ( here the base used is 10 ) and for any number of elements on the left hand side.

So the point is, if you have logarithmic tables that you could refer, any complex multiplication/division can be broken down into three simple steps and the answer might be found.

1. Take log of the numbers in the multiplication/division process ( X,Y...)the tables

2. Add/subtract the log values up ( x1 + y1, or x1 - y1 ..as appropriate )

3. Take the antilog of the values.. which is the same as ( 10^(x1+y1) or 10^(x1 - y1) ...ie X*Y, or X/Y ) and you have the answer.

Love and Light.

Answer 4

Anynumber can be written as
A^x.

Now the log of a number Y is X such that Y = A^X

So as you can see there is a base A involved. You can speak of natural log which is e^x (e = 2.7182...) or log base 10 (10^x).

Example

What is the log base 10 of 1000?
answer 3, because 10^3 = 1000

What is the natural log of 1000?
answer 6.9077... because 2.7182^6.9077=1000

Answer 5

when you say Log A(base on C)= B it means that C^B=A (C power B equals A)
for example you know that 10^2=100 so Log 100(base on 10)=2
and Ln is the log base on a number named "nepper" which ~2.7

Answer 6

Aspirin is a blood thinner and it motives the clotting time of the blood to strengthen. this signifies that if the affected individual began to bleed for the time of surgical procedure, the OR crew ought to have a a lot extra sturdy time controlling the bleed than if the affected individual were taking Tylenol. it truly is a sensible flow, and a level that ought to save a affected individual's existence.

Answer 7

we use notation log for base 10
we use notation ln when base is e
suppose 10^x=y
we define
log y=x ie to base 10