Quote Originally Posted by NickThissen View Post
You don't need to use logs, that's just silly. It boils down to the same thing in the end anyway (of course), you just use the root...

Suppose a and b are given and you need to solve for x:
x^a = b

Then x = b^(1/a).

In case a = 2, everyone knows this. If x^2 = b, then x = sqrt(b) = b^(1/2). Give or take a minus sign.
It's the same when a is not 2, you just take the 'a'th root instead of the square root.


Now logs...
You correctly state that
log(b) / log(x) = a.

But how does that help? Let's calculate...


And we get exactly the same result... So, useless, don't use logs



As for x^7 = 16384, the answer x = 4 is not the only answer, there are 6 more answers, but they are all complex:
WELL LOOK AT YOU MR. MATHEMATICS PERSON! Nice proof though. I guess you had some free time eh?

EDIT: I asked for a logarithmic proof because minitech's question involved logarithms. 'tis all.