[กิตติ]

$(log_ba)(log_dc)=1 \rightarrow \dfrac{\log a}{\log b}\dfrac{\log c}{\log d} =1 $

$\quad a^{log_bc-1} \quad b^{log_cd-1} \quad c^{log_da-1} \quad d^{log_ab-1}$

$= \dfrac{a^{log_bc}}{a} \dfrac{b^{log_cd}}{b}\dfrac{c^{log_da}}{c} \dfrac{d^{log_ab}}{d} $

$log_bc=log_ad$
$log_cd=log_ba$
$log_da=log_cb$
$log_ab=log_dc$

$= \dfrac{a^{log_ad}}{a} \dfrac{b^{log_ba}}{b}\dfrac{c^{log_cb}}{c} \dfrac{d^{log_dc}}{d}$

$= \dfrac{d}{a} \times \dfrac{a}{b} \times \dfrac{b}{c} \times \dfrac{c}{d}$

$=1$