This is a problem from my book:

"Let x = log3 2 and y = log3 10. Write each expression in terms of x and y."

and then one of the problems is log3 1/8


I have no idea what the hell they want me to do; I dont even see an x or a y in the expression they want me to write in terms of x and y, and my book isnt helping me.

Doesn't seem like there is much to do. If x = log3 (2), then 3^x = 2. that to me seems to be rewritten in terms of x. If you wanted to solve for an actual number, calculators generally use log10. So, log10 (3^x) = log10 (2), then x log10 (3) = log10 (2), then x = log10 (2) / log10 (3). That you can do in a calculator easily. For the other, the same ideas results in 3^y = 10, and in terms of log10, you get y = log10 (10) / log10 (3). Simplifying to y = 1 / log10 (3). Maybe I'm missing something, but 3^x = 2 and 3^y = 10 seems like all you need to do.

Holy crap. That post is a month old. I thought it said Jul 2, but it said Jun 2. I guess it's a bit late, now.

I know this is way too late, but here goes:

"Let x = log3 2 and y = log3 10. Write log3 (1/8) in terms of x and/or y."

First of all, log3 8 = log3 (2^3) = 3 (log3 2) = 3x.
Then, log3 (1/8) = (log3 1) - (log3 8) = -log3 8, since log3 1 = 0.

Hence log3 (1/8) = -3x.

Hope that helps, even though it's very late! :(

whoa that's from the aops book.