what is logarithms?

Question

how can i undestand logarithms better? i need some advise because i can't undestand what my teacher taught me. can anyone tell me how to understand logarithns and function better?

Answer 1

You might be best off reading the web pages listed in the other answers, but here's my very trivial explanation...

A log is a power run backwards. A power is a log run backwards.

I.E.

If 10^5 = 100000 then LOG-base10 (100000) = 5
conversely, if LOG-base2(127) = 7 then 2^7 = 127

Put in english, LOG-baseN(x) asks "To what power must I raise N to get x."

This is useful in all sorts of ways, but the most typical one is where you have an equation with a power, but the power is unknown..

12^x = 144, solve for x

So rearrange using a log to find the unknown power.
LOG12(144) = x.

Plug into your calculator and you get x = 2.

Notation:
Used alone, log() generally means base 10. ln() (natural log) means base e and logn() where n is a number can refer to any base you choose.

Answer 2

The log of a number to a given base is the power to which the base must be raised to give the number.
Example 1
100 = 10²
100 = number
10 = base
2 is power
log base ten of 100 = 2 (the power to which the base is raised)
Example 2
8 = 2³
log base 2 of 8 = 3 (the power to which the base is raised)
Hope these examples might help.

Answer 3

you define the logarithm of a (positive) number as the power to which you would have to raise a base to get that number.
To begin with you will mainly work with log to base 10

log 10 = 1; 10^1 = 10
log 100 = 2; 10^2 = 100
log 1 = 0; 10^0 = 1
log 0.1 = -1; 10^-1 = 1/10^1 = 0.1

the result of this definition is that log(xy) = log(x) + log(y)
so logs can make powers and multiplication easier, but addition and subtraction (of the numbers not hte logs) becomes harder.

Answer 4

Logarithms are nothing but expressing exponential functions differently for ex if y=e^x then x=log y(to the base a) which you will be writing near y left to it.they are used so that simplification can be done easily rather than working with exponents

Answer 5

i think a logarithm is where curved lines all pass through the same point on the x axis but i dont know how to explain soz

Answer 6

A logarithm is an exponent.

Answer 7

--- http://www.math.utah.edu/~pa/math/log.html
http://www.physics.uoguelph.ca/tutorials/LOG/
http://www-lmmb.ncifcrf.gov/~toms/paper/primer/latex/node2.html