Question

What is log(55)?

Answer 1

\[\log_b(a)=\frac{\ln(a)}{\ln(b)} \text{ <---change of base formula } \]

Answer 2

It is 4.0073331852324709186627029111913169393473082082059348.

Answer 3

@samarium

That is impossible, because 1 < log 55 < 2.

Answer 4

@Easyaspi314 http://www.wolframalpha.com/input/?i=log%2855%29

Answer 5

Is the base 10?

Answer 6

@myininaya
Does b represent 10 or e?

Answer 7

Some people understand that base to be 10 while some have the understanding it is e

Answer 8

@samarium

That is the value of ln 55. The question says log 55, which is understood to be base 10.

Answer 9

It depends on what notation that class is using.

Answer 10

Most likely it is 10 and @Easyaspi314 is correct then.

Answer 11

We saw it on a picture of a clock where it said log(55)=4 we had a problem with it too. So we asked you guys. I'm sitting right next to Aragorn48 in Web Design trying not to do work

Answer 12

@samarium

When natural logs are used, it would say ln 55. That is common notation in mathematics. And that is base e.

log 55 means base 10 (if no base is mentioned).

Answer 13

Web design is fun. Give me back my beret @samarium

Answer 14

In computer science, I have seen them use log(a) to mean ln(a).

Answer 15

Our Algebra 2 teacher told us log(x) is the common log and ln was the natural log

Answer 16

But there are also other different things in computer science. Like they like to include 0 in the natural numbers. :p

Answer 17

Yeah. we were told ln(a) is the natural log.

Answer 18

@myininaya

In the US, all mathematics classes use ln to represent base e, and log (without any base) is base 10.

Answer 19

@Easyaspi314 I don't know if all math classes do it because I have seen it mentioned differently in texts.
Would you like me to show you an example?

Answer 20

sure

Answer 21

@myininaya

Yes, please show me one US text in mathematics that used log to mean base e.

Answer 22

Of course, log of a number, can be converted to ln with "change of base". But an expression of ln is commonly understood to mean base e.

Answer 23

http://books.google.com/books?id=59d26G1_3ioC&pg=PA67&lpg=PA67&dq=cryptography+log%28a%29+natural+log&source=bl&ots=eFEAB4K8Jp&sig=lEIDo0ArUjo28paPeS6JipTWnQI&hl=en&sa=X&ei=APqAUsH0HsfZ2QXp4IC4BA&ved=0CEMQ6AEwBA#v=onepage&q=log%28a%29%20natural%20log&f=false
page 67

Answer 24

I agree it is common but I'm saying that it can have a different meaning.

Answer 25

@myininaya

Would appreciate if you can show me one US math text that uses log to mean base e. From the thousands of texts in mathematics, I have never seen one that uses ln to mean base 10.

Answer 26

Above.

Answer 27

I posted a link.

Answer 28

There is a text I used in my grad studies that also used log(a) to mean natural log of a.

Answer 29

@myininaya

In that post (from that text), the author prefaces by saying that he is using log to represent base e (for convenience purposes).

What I am saying is that if a student sees ln, it is to be understood base e. If a student just sees log, it is understood to mean base 10, unless another base is mentioned.

Answer 30

And of course there is also wolfram who understands the base to be e in log(55). Looks like wolfram is using the computer science terminology.

Answer 31

That is why I asked the person who asked the question what the notation meant. Teachers may I have different preferences on notation,

Answer 32

Exactly. But we are in "mathematics" where log is understood to be base 10. I was only talking about mathematics classes, not computer science or other disciplines.

Answer 33

Yep. It just depends on the notation. :)

Answer 34

or the meaning of.
in my classes i tell them to understand it as base 10 so they know what it means

Answer 35

but i also say just because i'm using this meaning for this notation doesn't mean it can't be used differently

Answer 36

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

Answer 37

Scroll down to particular bases and you will see it having different meaning for the notation.

Answer 38

The teacher must specify which one they are using in the class.