Question

If 2 to the power x = 3 to the power y = 6 to the power z , show that 1/x+1/y = 1/z

Answer 1

$HEYA \: \\ \\ 2 {}^{x} = 3 {}^{y} =6 {}^{z} = k \: \: let \: \\ \\ 2 = k {}^{1 \div x} \: \: ...Equation \: \: \: (i) \\ \\ 3 = k {}^{1 \div y} \: ...Equation \: \: (ii) \\ \\ 3 \times 2 = k {}^{1 \div z} \: ...Equation \: \: (iii) \\ \\ from \: i \: and \: ii \: we \: have \: \\ \\ k {}^{1 \div x} \times k {}^{1 \div y} = k {}^{1 \div z} \\ \\ on \: \: compare \: powers \: of \: k \: we \: have \: \\ \\ (1 \div x) + (1 \div y) = (1 \div z)$

HENCE PROVED