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

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