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log-3-12-a-log-3-18-

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} \\…

log-2-20-2-log-2-5-2-log-2-10-

Question Number 197254 by sciencestudentW last updated on 11/Sep/23 $$\frac{\left(\mathrm{lo}\underset{\mathrm{2}} {\mathrm{g}20}\right)^{\mathrm{2}} \:−\left(\mathrm{lo}\underset{\mathrm{2}} {\mathrm{g}5}\right)^{\mathrm{2}} \:}{\mathrm{lo}\underset{\mathrm{2}} {\mathrm{g}10}\:}=? \\ $$ Answered by AST last updated on 11/Sep/23 $$=\frac{\left({log}_{\mathrm{2}}…

log-2-a-log-3-b-log-72-

Question Number 197255 by sciencestudentW last updated on 11/Sep/23 $$\mathrm{log}\:\mathrm{2}={a} \\ $$$$\mathrm{log}\:\mathrm{3}={b} \\ $$$$\mathrm{log}\:\mathrm{72}=? \\ $$ Answered by AST last updated on 11/Sep/23 $${log}\left(\mathrm{9}×\mathrm{8}\right)=\mathrm{2}{log}\mathrm{3}+\mathrm{3}{log}\mathrm{2}=\mathrm{2}{b}+\mathrm{3}{a} \\…

log-6-2-a-log-6-9-

Question Number 197249 by sciencestudentW last updated on 11/Sep/23 $$\mathrm{lo}\underset{\mathrm{6}} {\mathrm{g}2}={a} \\ $$$$\mathrm{lo}\underset{\mathrm{6}} {\mathrm{g}9}=?\:\: \\ $$ Answered by AST last updated on 11/Sep/23 $$\frac{{log}\mathrm{2}}{{log}\mathrm{2}+{log}\mathrm{3}}={a}\Rightarrow{log}\mathrm{2}\left(\mathrm{1}−{a}\right)={alog}\mathrm{3} \\…

Question-197238

Question Number 197238 by sonukgindia last updated on 10/Sep/23 Commented by Frix last updated on 12/Sep/23 $$\mathrm{No}\:\mathrm{useful}\:\mathrm{exact}\:\mathrm{solution}. \\ $$$$\mathrm{Set}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{quarter}\:\mathrm{circle}\:=\mathrm{1} \\ $$$$\Rightarrow \\ $$$$\mathrm{Radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{semi}\:\mathrm{circle}\:\approx.\mathrm{717910784} \\ $$$${r}\approx.\mathrm{205269551}…