Couple of log questions

MadmanMurray

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

snipez90

What is the question? If it's to simplify as much as possible, you can use log(xy) = log(x) + log(y).

MadmanMurray

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?

NoMoreExams

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

tiny-tim

Hi MadmanMurray!

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!! )

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

and

2.) 2^x + 1 = 3^{2x - 1}

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

tiny-tim

Nooo … that woud be (logx²) +2

Hint: if loga = b, then a = e^b

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.

Delphi51

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.

kbaumen

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[tex]_{2}[/tex]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[tex]^{2}[/tex]) = 2.

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.

kbaumen

Oh. Thanks a lot for the explanation.

HallsofIvy

Then x²+ 2= a^2.6 where "a" is the base of the logarithm (probably 10 or e).

Since there exponentials are to different bases, which cannot be converted to one another, there is no easy way to solve this equation.

MadmanMurray

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.