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A-log-2-9-2-1-log-2-log-2-9-7-1-log-4-7-




Question Number 144387 by SOMEDAVONG last updated on 25/Jun/21
A=((log_2 9)^2 )^(1/(log_2 (log_2 9))) ×((√7))^(1/(log_4 7)) =?
$$\mathrm{A}=\left(\left(\mathrm{log}_{\mathrm{2}} \mathrm{9}\right)^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{2}} \left(\mathrm{log}_{\mathrm{2}} \mathrm{9}\right)}} ×\left(\sqrt{\mathrm{7}}\right)^{\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{4}} \mathrm{7}}} =? \\ $$
Answered by liberty last updated on 25/Jun/21
(1/(log _2 (log _2 9)))=log _((log _2 9)) (2)  ⇒A=((log _2 9)^(log _((log _2 9)) (2)) )^2 ×(7^(log _7 (4)) )^(1/2)   ⇒A= 4×(√4) = 8.
$$\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{log}\:_{\mathrm{2}} \mathrm{9}\right)}=\mathrm{log}\:_{\left(\mathrm{log}\:_{\mathrm{2}} \mathrm{9}\right)} \left(\mathrm{2}\right) \\ $$$$\Rightarrow\mathrm{A}=\left(\left(\mathrm{log}\:_{\mathrm{2}} \mathrm{9}\right)^{\mathrm{log}\:_{\left(\mathrm{log}\:_{\mathrm{2}} \mathrm{9}\right)} \left(\mathrm{2}\right)} \right)^{\mathrm{2}} ×\left(\mathrm{7}^{\mathrm{log}\:_{\mathrm{7}} \left(\mathrm{4}\right)} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$$\Rightarrow\mathrm{A}=\:\mathrm{4}×\sqrt{\mathrm{4}}\:=\:\mathrm{8}. \\ $$
Commented by SOMEDAVONG last updated on 25/Jun/21
Thanks sir!
$$\mathrm{Thanks}\:\mathrm{sir}! \\ $$

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