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Question-211191




Question Number 211191 by Tawa11 last updated on 30/Aug/24
Answered by mm1342 last updated on 30/Aug/24
((2^x )^y )^x =(3^y )^z =7^z =11 ✓
$$\left(\left(\mathrm{2}^{{x}} \right)^{{y}} \right)^{{x}} =\left(\mathrm{3}^{{y}} \right)^{{z}} =\mathrm{7}^{{z}} =\mathrm{11}\:\checkmark \\ $$$$ \\ $$
Commented by Tawa11 last updated on 30/Aug/24
Thanks sir.  I appreciate.
$$\mathrm{Thanks}\:\mathrm{sir}. \\ $$$$\mathrm{I}\:\mathrm{appreciate}. \\ $$
Answered by gri_bor last updated on 30/Aug/24
  x=log_2 3  y=log_3 7  z=log_7 11  2^(xyz) =2^(log_2 3×log_3 7×log_7 11) =2^(log_2 7×log_7 11)   =2^(log_2 11) =11
$$ \\ $$$${x}={log}_{\mathrm{2}} \mathrm{3} \\ $$$${y}={log}_{\mathrm{3}} \mathrm{7} \\ $$$${z}={log}_{\mathrm{7}} \mathrm{11} \\ $$$$\mathrm{2}^{{xyz}} =\mathrm{2}^{{log}_{\mathrm{2}} \mathrm{3}×{log}_{\mathrm{3}} \mathrm{7}×{log}_{\mathrm{7}} \mathrm{11}} =\mathrm{2}^{{log}_{\mathrm{2}} \mathrm{7}×{log}_{\mathrm{7}} \mathrm{11}} \\ $$$$=\mathrm{2}^{{log}_{\mathrm{2}} \mathrm{11}} =\mathrm{11} \\ $$
Commented by Tawa11 last updated on 30/Aug/24
Thanks sir.  I appreciate.
$$\mathrm{Thanks}\:\mathrm{sir}. \\ $$$$\mathrm{I}\:\mathrm{appreciate}. \\ $$

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