11/12   On paper, how do you figure out what log_2 (4/3) is? I remember
        log_2 (4/3) = log_2 4 - log 3 = 2 - log 3. Now what?
        \_ 2 - log_2 3 = 2 - ln 3 / ln 2.  Then get a mathematical table and
           look up ln 3 and ln 2.  Or use a polynomial of ln(1+x).  I forgot
           the polynomial.  --- yuen
           \_ ln(1+x) = x + x^2/2 + x^3/3 + x^4/4 + ..., for |x| < 1.
              As another poster pointed out, log_2(4/3) = ln(4/3)/ln(2)
              \_ That polynomial is wrong.  Try ln(1 + 0.9).
              \_ It should be ln(1+x) = x/1 - x^2/2 + x^3/3 - x^4/4 + ...
           \_ that was remarkably useless.
              \_ How else would you do that?
                 \_ perhaps they mean the question, and therefore the whole
                \_ real?  imaginary?  quaternion?  octonion?
                    thread is useless, which it is.
        \_ Here:
           log_X (Y) = log_anything(Y) / log_anything(X)
           where anything is, well, any number.
           \_ real?  imaginary?  quaternion?  octonion?  sedenion?
              \_ Yes, for any reasonable definition of the "log_X (Y)" symbol
                 over these domains. For domains more general than positive
                 reals where a "log" is still definable, Log becomes
                 multivalued... which only results in the above
                 holding for "some appropriate" branch thereof. -alexf
              \_ Damn, look who looked at a fancy math book
                 for a few hefty terms. I'm surprised you were
                 even able to spell those words correctly.
              \_ If you wanted to show off, you could simply say
                 "non-positive?" instead of throwing out all the other terms.
                 Besides, you should've said "complex?" instead of "imaginary?"
                 to make your progression of terms correct.
                 \_ alexf insults deleted
           \_ But then how do you proceed on paper?  Same problem.
        \_ how accurate do you need to be?  you can get a rough approximation
           using differentials.
           \_ just use a fucking calculator.
                \_ no calculator on the GRE