Question Number 197253 by sciencestudentW last updated on 11/Sep/23
$$\mathrm{lo}\underset{\mathrm{3}} {\mathrm{g}12}={a} \\ $$$$\mathrm{log}\underset{\mathrm{3}} {\:}\mathrm{18}=?\: \\ $$
Answered by AST last updated on 11/Sep/23
$$\frac{{log}\mathrm{3}+\mathrm{2}{log}\mathrm{2}}{{log}\mathrm{3}}={a}\Rightarrow\mathrm{2}{log}\mathrm{2}=\left({a}−\mathrm{1}\right){log}\mathrm{3} \\ $$$$\frac{{log}\mathrm{2}+\mathrm{2}{log}\mathrm{3}}{{log}\mathrm{3}}=\frac{{log}\mathrm{2}}{{log}\mathrm{3}}+\mathrm{2}=\frac{{a}−\mathrm{1}}{\mathrm{2}}+\mathrm{2}=\frac{{a}+\mathrm{3}}{\mathrm{2}} \\ $$