1.

`2^x =5^y=10^(-z)`. find `(1/x+1/y+1/z)`

Answer» Let `2^x = 5^y = 10^-z = k`
Taking log for each value,
`xlog2 = logk => x = logk/log2 = log_2k => 1/x = log_k2`
`ylog5 = log k => y = log_5k => 1/y = log_k5`
`-zlog10 = logk => -z = log_10k => 1/z = log_k(1/10)`
`:. 1/x+1/y+1/z = log_k2+ log_k5+log_k(1/10) = log_k(2**5**1/10) = log_k1 = 0`
`:.1/x+1/y+1/z = = 0`


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