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Question

2^x=3^y=6^z ,then 1/z = 1/x +1/y is

a. true
b. false
c. cant say
d. data insufficient 

Posted by: Saptarshi Bhattacharya in Olympiad{RMO+INMO+IMO} 5 years ago, Total Answer(s): 2

Answer(s)

2^x=3^y

on taking log both sides 

x=ylog3/log2    ...(i)

3^y=6^z

on taking log both sides 

z=ylog3/log6   ...(ii)

putting (i)  and (ii)  in 1/z=1/x+1/y

LHS=RHS 

a. is answer 

By: Dinesh Ramswami, 4 years ago

2^x=3^y=6^z=k

2^x=k           3^y=k           6^z=k

2=k^(1/x)      3=k^(1/y)      6=k^(1/z)

2 * 3 = 6

k^(1/x) * k^(1/y) = k^(1/z)         (Substituting the values)

k^((1/x)+(1/y)) = k^(1/z)

1/x+1/y=1/z

Therefore (a) is the correct answer

By: Son Goku, 3 years ago

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