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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?