An algebra problem by Kunal Jain
Algebra
Level
2
If 5^x = 3^y = 45^z , then 1/z is equal to ?
2/x+2/y
1/x+2/y
2/x+1/y
1/x+1/y
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1 solution
if 5^x=3^y=45^z=k
then 5=k^(1/x), 3=k^(1/y) and 45=k^(1/z)
45=3X3X5
k^(1/z)=k^(1/x) k^(1/y) k^(1/y)
k^(1/z)=k^(1/x)*k^(2/y)
k^(1/z)=k^(1/x+2/y)
1/z=1/x+2/y