Question Number 159345 by akolade last updated on 15/Nov/21
Answered by Ar Brandon last updated on 15/Nov/21
$$\mathrm{5}^{\frac{\mathrm{y}}{\mathrm{2}}+\mathrm{3}} =\mathrm{125}\left(\mathrm{5}^{\frac{\mathrm{y}}{\mathrm{2}}} \right)=\mathrm{125}\left(\mathrm{5}^{\mathrm{y}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$$=\mathrm{125}\left(\mathrm{36}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} =\mathrm{125}×\mathrm{6}=\mathrm{750} \\ $$
Commented by akolade last updated on 15/Nov/21
$$\mathrm{cool}\:\mathrm{sir} \\ $$
Answered by yeti123 last updated on 16/Nov/21
$$\mathrm{5}^{{y}} \:=\:\mathrm{36} \\ $$$${y}\:=\:\mathrm{log}_{\mathrm{5}} \:\mathrm{36} \\ $$$$ \\ $$$${x}\:=\:\mathrm{5}^{\frac{{y}}{\mathrm{2}}\:+\:\mathrm{3}} \\ $$$$\mathrm{log}_{\mathrm{5}} \:{x}\:=\:\mathrm{log}_{\mathrm{5}} \:\left(\mathrm{5}^{\frac{{y}}{\mathrm{2}}\:+\:\mathrm{3}} \right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\left(\frac{{y}}{\mathrm{2}}\:+\:\mathrm{3}\right)\:\mathrm{log}_{\mathrm{5}} \:\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{{y}}{\mathrm{2}}\:+\:\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}_{\mathrm{5}} \:\mathrm{36}\:+\:\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{log}_{\mathrm{5}} \:\mathrm{36}^{\mathrm{1}/\mathrm{2}} \:+\:\mathrm{log}_{\mathrm{5}} \:\mathrm{5}^{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{log}_{\mathrm{5}} \:\mathrm{6}\:+\:\mathrm{log}_{\mathrm{5}} \:\mathrm{125} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{log}_{\mathrm{5}} \:\left(\mathrm{6}×\mathrm{125}\right) \\ $$$$\:\:\:\:\:\:{x}\:\:\:\:=\:\mathrm{6}×\mathrm{125} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{750} \\ $$