What are the basic, fundamental concepts of logarithms? Soon I will be learning of logarithms, but

da1intobp

da1intobp

Answered question

2022-06-01

What are the basic, fundamental concepts of logarithms?
Soon I will be learning of logarithms, but I wish to have a head start over my class mates or at least a fair greeting to the concept. I would appreciate a very clear-cut answer with very straight to the point examples, an answer like this and with steps would be tremendously helpful and quickly voted best answer. Some specific questions on which to base your answer could be: why are they used? What is an example of a simple logarithm? how do you solve one?, and how does it apply to quadratic equations? Thanks in advance.

Answer & Explanation

Gillian Krueger

Gillian Krueger

Beginner2022-06-02Added 1 answers

Often in math you want to know what power you have to raise b to in order to get x as a result:
b ? = x .
This question is so basic that it comes up all the time. The answer to this question is called the logarithm (base b) of x.
For example, 10 to what power is 1000? The answer is log 10 ( 1000 ) = 3
The name "logarithm" is undescriptive and intimidating. A more descriptive name might be "the exponent from b to x."
log b ( x ) = the exponent from  b  to  x .
Hana Medina

Hana Medina

Beginner2022-06-03Added 1 answers

A large part of mathematics is devoted to finding solutions to some equation. Given y find x such that:
f ( x ) = y .
This is accomplished by finding (or getting information about) the inverse of the function f. When f contains a power function a b you are required to invert the power operation. When you want to solve for the base x b = y the inverse is the b-th root function x = y b . When you want to invert with respect to the exponent a x = y the inverse function is called logarithm: x = log a y
Notice that since a b can be written as e b log e a (this you will learn, but you can find yourself if you work a little bit), every power can be expressed by means of the exponential function exp ( x ) = e x where e is a fixed number. So every power and inverse of a power can be written by means of exponential and logarithmic functions.
Logarithm were historically very important because they convert multiplications into sums (as exponentiation converts sums into products):
log ( a b ) = log a + log b
and powers into multiplications:
log ( a b ) = b log a .
Hence if you have a tool to compute logarithms (in any fixed base) you are able to simplify this kind of computations. The tools used (before calculators) were the logarithmic tables and the slide rule.

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