Question

Prove that: `(1)/("log"_2 30) + (1)/("log"_3 30) + (1)/("log"_5 30)` = 1

Answer 1

L.H.S.
= `(1)/("log"_2 30) + (1)/("log"_3 30) + (1)/("log"_5 30)`

= `(1)/(("log"30)/("log"2)) + (1)/(("log"30)/("log"3)) + (1)/(("log"30)/("log"5))`

= `("log"2)/("log"30) + ("log"3)/("log"30) + ("log"5)/("log"30)`

= `(1)/("log"30)("log"2 + "log"3 + "log"5)`

= `(1)/("log"(2 xx 3 xx 5)) ("log"2 + "log"3 + "log"5)`

= `(("log"2 + "log"3 + "log"5))/(("log"2 + "log"3 + "log"5)`
= 1
= L.H.S.
Hence proved.