Question Number 171854 by Mikenice last updated on 21/Jun/22
$${solve}: \\ $$$$\left(\mathrm{3}\sqrt{\mathrm{2}}\right)^{{n}} =\mathrm{3} \\ $$
Answered by Rasheed.Sindhi last updated on 21/Jun/22
$$\left(\mathrm{3}\sqrt{\mathrm{2}}\right)^{{n}} =\mathrm{3} \\ $$$${n}\mathrm{log}\left(\mathrm{3}\sqrt{\mathrm{2}}\right)=\mathrm{log}\:\mathrm{3} \\ $$$${n}=\frac{\mathrm{log}\:\mathrm{3}}{\mathrm{log}\left(\mathrm{3}\sqrt{\mathrm{2}}\right)}\:=\frac{\mathrm{log}\:\mathrm{3}}{\mathrm{log}\:\mathrm{3}+\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{log}\:\mathrm{2}} \\ $$