SOLUTION: a^x =b^y = c^z = abc ; find 1/x + 1/y + 1/z

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Question 841748: a^x =b^y = c^z = abc ; find 1/x + 1/y + 1/z
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
taking logs then dividing we can see that...

x=ln%28abc%29%2Fln%28a%29
from which we deduce
1%2Fx=ln%28a%29%2Fln%28abc%29
similarly
1%2Fy=ln%28b%29%2Fln%28abc%29
and
1%2Fz=ln%28ac%29%2Fln%28abc%29
therefore
1%2Fx%2B1%2Fy%2B1%2Fz=%28ln%28a%29%2Bln%28b%29%2Bln%28c%29%29%2Fln%28abc%29=1
i.e.
1%2Fx%2B1%2Fy%2B1%2Fz=1