12 = 3*4
Substitute the values and simplify.
3^x = 4^y = 12^z,
that z = xy/(x+y)
Tried looking at 3^x = 4^y and taking log base 12 to eliminate one of the variables, ending up with x=ylog base 3 (4).
then I looked at 4^y = 12^z, took log base 12 as well, and ended up with z= y*log base 12 (4).
Plugged x and y into xy/(x+y), but couldnt get it to equal z
had a fiddle about with it, but I can't seem to prove it. maybe, im thinking too hard, anybody else got ideas?