Question

2powerx=3powery=6 power(-z) then(1/x)+(1/y)+(1/z)=?

Answer 1

$2^x=6^{-z}=2^{-z}3^{-z}\\\\2^{x+z}=3^{-z}\\\\(x+z)\ Log\ 2=(-z)Log\ 3\ \ ...(1)\\\\2^x=3^y\\\\x\ Log\ 2=y\ Log\ 3\ \ ...(2)\\\\(1) \div (2) \implies \frac{x+z}{x}=\frac{-z}{y}\\\\SO\ xy+yz+zx=0\\\\Divide\ by\ xyz\\\\\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0$