Examples of Math Problems: a^x =b^y = c^z = abc ; find 1/x + 1/y + 1/z

Monday, April 21, 2014

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

Taking logs then dividing we can see that...

x=ln%28abc%29%2Fln%28a%29

x=ln%28abc%29%2Fln%28a%29

from which we deduce
1%2Fx=ln%28a%29%2Fln%28abc%29

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

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