Question

2^x=5^y=10^z prove that 1/x+1/y=1/z​

Answer 1

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Step-by-step explanation:

$2^x=10^z\\x=z\log_2{10}$ and $5^y=10^z\\y=z\log_510$

So

$\frac1x+\frac1y=\frac1{z\log_2{10}}+\frac1{z\log_5{10}}=\frac1z(\log_{10}2+\log_{10}5)=\frac1z(\log_{10}10)=\frac1z$