Question Number 12093 by uni last updated on 13/Apr/17
$$\mathrm{log}_{\mathrm{abc}} \mathrm{b}=\mathrm{3} \\ $$$$\mathrm{log}_{\mathrm{abc}} \mathrm{c}=\mathrm{4} \\ $$$$\mathrm{log}_{\mathrm{abc}} \mathrm{a}=? \\ $$
Answered by ajfour last updated on 13/Apr/17
$$\mathrm{log}\:_{{abc}} {abc}\:=\left(\mathrm{log}\:_{{abc}} {a}\right)+\left(\mathrm{log}\:_{{abc}} {b}\right)+\left(\mathrm{log}\:_{{abc}} {c}\right)=\mathrm{1} \\ $$$$\left(\mathrm{log}\:_{{abc}} {a}\right)+\mathrm{3}+\mathrm{4}\:=\mathrm{1} \\ $$$$\mathrm{log}\:_{{abc}} {a}\:=−\mathrm{6}\:. \\ $$$$ \\ $$$$ \\ $$