## Couple of log questions

1. The problem statement, all variables and given/known data
1.) 3logx2y + 2logxy
2.) 4logabc - 2loga2b - 3logbc

2. Relevant equations

3. The attempt at a solution
I know that 3logx2 is the same as 6logx but I don't know what to do since theres a y there
 What is the question? If it's to simplify as much as possible, you can use log(xy) = log(x) + log(y).
 Yep thats the question. I'm just confused about what to do with all these coefficients. Is 3logx2y the same as logx6y3?? Can I write logx6y3 as logx[sup]6[/sup + log]y3 or do I have to get rid of them powers first?

## Couple of log questions

Yes assuming x^2y are both an argument of your log

Blog Entries: 27
Recognitions:
Gold Member
Homework Help
 Quote by MadmanMurray Can I write logx6y3 as logx6 + logy3 or do I have to get rid of them powers first?

I'm guessing that they want it in the form 6logx + 3logy.

(after all, how would you look up logx6 in log-tables if x = 2.345? … you'd have to find 2.3456 first, and the only way of doing that is to … yes!! )
 Thanks a lot. I have 2 more log questions in front of me that are confusing as hell too: 1.) log (x2 + 2) = 2.6 and 2.) 2x + 1 = 32x - 1 For the first one there I was wondering if I can express it like this 2logx + 2? Can I do that?

Blog Entries: 27
Recognitions:
Gold Member
Homework Help
 Quote by MadmanMurray 1.) log (x2 + 2) = 2.6 … I was wondering if I can express it like this 2logx + 2? Can I do that?
Nooo … that woud be (logx2) +2

Hint: if loga = b, then a = eb
 Careful tiny-tim: log(a) doesn't necessarily refer to the natural logarithm. log(a) commonly refers to the logarithm base 10 as well.
 Recognitions: Homework Help if log X = Y, then X = B^Y (where B is the base of the log) If it doesn't make sense in logarithm land, transform it to power land! And vice versa.

 Quote by jgens Careful tiny-tim: log(a) doesn't necessarily refer to the natural logarithm. log(a) commonly refers to the logarithm base 10 as well.
Well, where I study lg is decimal logarithm, ln is natural logarithm and log refers to a logarithm with any other base which is shown in subscript right after the log symbol. For example log$$_{2}$$8 = 3 ( I don't know why, but using LaTex here shows a subscript as a superscript on my machine. The 2 is supposed to be as a subscript. I hope you get the idea), lg100 = 2 and ln(e$$^{2}$$) = 2.

Blog Entries: 27
Recognitions:
Gold Member
Homework Help
 Quote by kbaumen For example log$_{2}$8 = 3 ( I don't know why, but using LaTex here shows a subscript as a superscript on my machine.
Hi kbaumen!

You have to use "inline" LaTeX (typing "itex" instead of "tex") if you're inserting into a line of text (see just above) …

but it's much better, on this forum, to use the X2 or X2 tags (just above the reply box), especially since any LaTeX takes up a lot of space on the server.

 Quote by tiny-tim Hi kbaumen! You have to use "inline" LaTeX (typing "itex" instead of "tex") if you're inserting into a line of text (see just above) … but it's much better, on this forum, to use the X2 or X2 tags (just above the reply box), especially since any LaTeX takes up a lot of space on the server.
Oh. Thanks a lot for the explanation.

Recognitions:
Gold Member
Staff Emeritus
 Quote by MadmanMurray Thanks a lot. I have 2 more log questions in front of me that are confusing as hell too: 1.) log (x2 + 2) = 2.6
Then x2+ 2= a2.6 where "a" is the base of the logarithm (probably 10 or e).

 and 2.) 2x + 1 = 32x - 1
Since there exponentials are to different bases, which cannot be converted to one another, there is no easy way to solve this equation.

 For the first one there I was wondering if I can express it like this 2logx + 2? Can I do that?

 Quote by HallsofIvy Since there exponentials are to different bases, which cannot be converted to one another, there is no easy way to solve this equation.
I decided to plug in some random numbers and the first one I plugged in (1) happened to work. Since theres no simple way to solve it maybe thats what I was meant to do.