Question Number 197252 by sciencestudentW last updated on 11/Sep/23
$$\mathrm{lo}\underset{{a}} {\mathrm{g}}{x}=\mathrm{30} \\ $$$$\mathrm{lo}\underset{{b}} {\mathrm{g}}{x}=\mathrm{70} \\ $$$$\mathrm{lo}\underset{{ab}} {\mathrm{g}}{x}=?\:\:\: \\ $$
Answered by AST last updated on 11/Sep/23
$$\frac{{logx}}{{loga}}=\mathrm{30};\frac{{logx}}{{logb}}=\mathrm{70}\Rightarrow\frac{{logb}+{loga}}{{logx}}=\frac{\mathrm{1}}{\mathrm{21}} \\ $$$$\Rightarrow{log}_{{ab}} {x}=\frac{{logx}}{{loga}+{logb}}=\mathrm{21} \\ $$