Logarithms, Explained - Steve Kelly

Translator: Hekim Atay Reviewer: Mehmet Sıddık Dilek

How does the difference between

Cudatiya navbera 0, 0000000398 û

point 0000000398 and

point 00000000398

0,00000000398'ê çawa dibe sedema

cause one to have red eyes after swimming?

çavsoriya piştê avjeniyê?

To answer this, we first need a way of

Ji bo bersiva vê,

dealing with rather small numbers,

ji bo ceribandina hejmarên piçûk û mezin

or in some cases extremely large numbers.

rêyek hewce ye.

This leads us to the concept of logarithms.

Ev jî têgeha Logarîtmayê tîne bîra me.

Well, what are logarithms?

Logarîtma çi ye?

Let's take the base number, b,

Hejmara bingeh b

and raise it to a power, p,

ya li ser "p"yê hildin.

like 2 to the 3rd power,

wek mînak 3 li ser 2yê

and have it equal a number n.

Ev jî yeksanê "n"yê be.

We get an exponential equation: b raised to the p power, equals n.

yeksaniyek heye: ser b yê p yeksan n ye.

In our example, that'd be 2 raised

di mînakê de, ev 3 li ser 2yê ye,

to the 3rd power, equals 8.

yeksanê 8ê ye.

The exponent p is said to be

"p"ya ku hejmara ser e,

the logarithm of the number n.

logarîtmaya "n"yê ye.

Most of the time this would be written:

Ev wiha jî tê nivîsîn "Logarîtma li bin b

"log, base b, of a number equals p, the power."

yeksanê "p"ya li ser e."

This is starting to sound a bit confusing with all the variables,

Mesele hinekî tevlihev dibe,

so let's show this with an example.

Lewma em mînakekê bidin

What is the value of

Bin log 10 nirxa 10.000'î çi ye?

log base 10 of 10,000?

The same question could be asked using exponents:

Wiha jî dikarî bipirsî:

"10 raised to what power is 10,000?"

Li ser 10î çend, dike 10.000?

Well, 10 to the 4th is 10,000.

Li ser 10î 4 dike 10.000

So, log base 10 of 10,000

Ango, bingeha 10ê log 10.000

must equal 4.

yeksanê 4an e.

This example can also be completed very simply on a scientific calculator.

Ev hesab bi makînê, bi hesanî tê hesabkirin

Log base 10 is used so frequently

Logarîtmayên bingeh 10,

in the sciences

di zanistîyê de hingî tê bikaranîn

that it has the honor of having its own button on most calculators.

di gelek makînayan de cihê wê taybet e.

If the calculator will figure out logs for me,

Mafir makîneyên bersê vê hesab dikin,

why study them?

em çima mijul dibin? niha bibêjim;

Just a quick reminder:

the log button only computes logarithms of base 10.

Tûşa log tenê bi bingeha 10î hesab dike.

What if you want to go into computer science

Hûn bi zanistiya computerê re têkildar bin

and need to understand base 2?

û bingeha 2yê hewce be?

So what is log base 2 of 64?

Log 64 bi bingeha 2yan çi ye?

In other words, 2 raised to what power is 64?

Ango, li ser 2yan çend, 64 e?

Well, use your fingers. 2, 4, 8, 16, 32, 64.

Bi tiliyan bijmirin, 2, 4, 8, 16, 32, 64.

Ango bi bingeha 2yan, log 64 yeksanê 6ê ye

So log base 2 of 64 must equal 6.

So what does this have to do with my eyes turning red

Çima çavê me hinan sor dibin, hinan nabin?

in some swimming pools

Çi têkiliya vê heye?

and not others?

Well, it leads us into an interesting

Li vir, têkiliyeke ecêb ya

use of logarithms in chemistry:

logarîtma û kîmyayê heye.

finding the pH of water samples.

dîtina pH'ê

pH asîdtî û bazîkiyê eşkere dike.

pH tells us how acidic or basic a sample is,

and can be calculated with the formula:

Formûl;

pH equals negative log base 10 of the hydrogen ion concentration, or H plus.

pH= -log10 [+H]

We can find the pH of water samples

pH'a Avên tîrîtiya hîdrojenê 0, 0000000398

with hydrogen ion concentration of point 0000000398

û 00000000398

and point 00000000398

bi makînê bibînin.

quickly on a calculator.

Punch: negative log of each of those numbers,

Dûre -logarîtmaya wan hildin.

and you'll see the pH's are 7.4 and 8.4.

pH 7,4 û 8,4 dertê.

Since the tears in our eyes have a pH of about 7.4,

pH'a hêsirê 7,4 e

the H plus concentration of .0000000398

0,70398 H

will feel nice on your eyes,

ji çavan re baş tê,

but the pH of 8.4 will make you feel itchy and red.

8,4 pH çavan sor dike û dixurîne.

"logarîtmaya "n"ya bi bingeha "b"yê yeksanê "p"yê ye.

It's easy to remember logarithms "log base b of some number n equals p"

by repeating: "The base raised to what power equals the number?"

dubare bikin: "li ser çendan yeksanê wê ye?"

"The BASE raised to what POWER equals the NUMBER?"

"Li ser(p) çendan (b) yeksanê wê(n) ye.

So now we know logarithms are very powerful

Êdî em dizanin, Logarîtma

when dealing with extremely small or large numbers.

ji bo hesabkirina hejmarê pir biçûk û mezin gelek bi kêr tê.

Hetta ku, hûn dikarin logarîtmayê

Logarithms can even be used

instead of eyedrops after swimming.

piştê avjeniyê wek derman bikarînin.