Question Number 71134 by Mr. K last updated on 11/Oct/19
$${if}\:{a},\:{b}\:{and}\:{c}\:{are}\:{positive},\:{find}: \\ $$$$\left(\frac{{a}}{{b}}\right)^{{log}_{\mathrm{10}} {c}} ×\left(\frac{{b}}{{c}}\right)^{{log}_{\mathrm{10}} {a}} ×\left(\frac{{c}}{{a}}\right)^{{log}_{\mathrm{10}} {b}} \\ $$$$ \\ $$
Answered by MJS last updated on 12/Oct/19
$$\mathrm{log}\:{x}^{\mathrm{log}\:{y}} =\mathrm{log}\:{y}\:\mathrm{log}\:{x}\:=\mathrm{log}\:{y}^{\mathrm{log}\:{x}} \:\Rightarrow\:{x}^{\mathrm{log}\:{y}} ={y}^{\mathrm{log}\:{x}} \\ $$$$\Rightarrow\:\mathrm{answer}\:=\mathrm{1} \\ $$