32^x=2, what's x? Please list all possible ways to solve it.?

Using logs, take the log of both sides:

log 32^x = log 2

Using log laws - (loga^b = b loga):

x log 32 = log 2

Simply divide both sides by log 32 to get x by itself:

x = log 2 / log 32

x = 0.2

Take logs to base 2
x log 32 = log 2
5x = 1
x = 1/5

32^x = 2
32 = 2^(1/x)
2^5 = 2^(1/x)
5 = 1/x
5x = 1
x = 1/5 (0.2)

x = 1/5 is the answer,

It's hard to explain how to get this and I don't really know myself but you can just try options on you calculator and enventually you should get one that = 2, for example I tried 32^1/6 and it wasn't quite right, then i tried 1/5 and it did equal 2 so it is right.

A bit of logic behind the answer is 2 x 1 = 2 and 2 x 2 x 2 x 2 x 2 (timesing 2 five times) = 32 so therefore 1/5!

Hope this helps you! =]