If 300=100[2^(x/3)], then x= ?
(The method is more important than the answer.)

like always in algebra, the way to solve this problem is to simplify
by doing the same thing to both sides of the equation.

300=100[2^(x/3)]

first, let's divide both sides by 100:

3 = 2^(x/3)

now we'll take the log base 2 of both sides.  (and, of course, we'll
remember that log2(2^z) = z, right?)

log2(3) = x / 3.

now, if we multiply both sides by 3, we see that

x = 3 * log2(3).

Google's handy calculator doesn't know how to take logs with the base
2, only e or 10, so we'll have to use the formula that log2(z) =
log(z) / log(2).

typing log(3)/log(2) into Google gives log2(3) = 1.5849625, so our answer is...

x = 4.7548875.

you can check that this is about right by remembering that 2^1 = 2,
2^2 = 4, so 2^1.58... should be somewhere between 2 and 4.

searching for "dr math logarithms" found this page

http://mathforum.org/library/drmath/sets/mid_logs.html

with lots of good questions & answers about logarithms.

good luck!

--David

Thanks for the links!