Question

If $\frac{\log x}{a}=\frac{\log y}{2}=\frac{\log z}{5}=kand{x}^4{y}^3{z}^{-2}=1$, find 'a'

Answer 1

$\log x=ak,\Rightarrow x=e^{ak}$

Similarly $\Rightarrow y=e^{2k}$

$\Rightarrow z=e^{5k}$

$\Rightarrow {\left(e^{ak}\right)}^4{\left(e^{2k}\right)}^3{\left(e^{5k}\right)}^{-2}=1$

$\Rightarrow e^{10ak-10ak}=e^0$, which is always equal to 1 irrespective of value of 'a'

$\Rightarrow a\in (-\infty ,\infty )$