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Question Number 49691 by Rio Michael last updated on 09/Dec/18

simplify ((log_3 64 × log_4 243)/(log_2 16))

$${simplify}\:\frac{{log}_{\mathrm{3}} \mathrm{64}\:×\:{log}_{\mathrm{4}} \mathrm{243}}{{log}_{\mathrm{2}} \mathrm{16}} \\ $$

Answered by math1967 last updated on 09/Dec/18

((log_3 4^3 ×log_(4 ) 3^5 )/(log_2 2^4 ))=((3log_(3  ) 4×5log_4 3)/(4log_2 2))  =((3×5log_3 4×log_4 3)/(4×1))=((15×1)/4)=3.75ans

$$\frac{{log}_{\mathrm{3}} \mathrm{4}^{\mathrm{3}} ×{log}_{\mathrm{4}\:} \mathrm{3}^{\mathrm{5}} }{{log}_{\mathrm{2}} \mathrm{2}^{\mathrm{4}} }=\frac{\mathrm{3}{log}_{\mathrm{3}\:\:} \mathrm{4}×\mathrm{5}{log}_{\mathrm{4}} \mathrm{3}}{\mathrm{4}{log}_{\mathrm{2}} \mathrm{2}} \\ $$$$=\frac{\mathrm{3}×\mathrm{5}{log}_{\mathrm{3}} \mathrm{4}×{log}_{\mathrm{4}} \mathrm{3}}{\mathrm{4}×\mathrm{1}}=\frac{\mathrm{15}×\mathrm{1}}{\mathrm{4}}=\mathrm{3}.\mathrm{75}{ans} \\ $$

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