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Question-55166




Question Number 55166 by Gulay last updated on 18/Feb/19
Answered by kaivan.ahmadi last updated on 18/Feb/19
3^(1+log_3 2) =3^(log_3 3+log_3 2) =3^(log_3 6) =6  and  2^(3log_2 5) =2^(log_2 5^3 ) =5^3 =125  and  4^(log_2 3) =(2^2 )^(log_2 3) =2^(2log_2 3) =2^(log_2 3^2 ) =3^2 =9
$$\mathrm{3}^{\mathrm{1}+{log}_{\mathrm{3}} \mathrm{2}} =\mathrm{3}^{{log}_{\mathrm{3}} \mathrm{3}+{log}_{\mathrm{3}} \mathrm{2}} =\mathrm{3}^{{log}_{\mathrm{3}} \mathrm{6}} =\mathrm{6} \\ $$$${and} \\ $$$$\mathrm{2}^{\mathrm{3}{log}_{\mathrm{2}} \mathrm{5}} =\mathrm{2}^{{log}_{\mathrm{2}} \mathrm{5}^{\mathrm{3}} } =\mathrm{5}^{\mathrm{3}} =\mathrm{125} \\ $$$${and} \\ $$$$\mathrm{4}^{{log}_{\mathrm{2}} \mathrm{3}} =\left(\mathrm{2}^{\mathrm{2}} \right)^{{log}_{\mathrm{2}} \mathrm{3}} =\mathrm{2}^{\mathrm{2}{log}_{\mathrm{2}} \mathrm{3}} =\mathrm{2}^{{log}_{\mathrm{2}} \mathrm{3}^{\mathrm{2}} } =\mathrm{3}^{\mathrm{2}} =\mathrm{9} \\ $$
Commented by Gulay last updated on 19/Feb/19
thank you sir
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir} \\ $$$$ \\ $$

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