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The number `N=(1+2log_(3)2)/((1+log_(3)2)^(2))+(log_(6)2)^(2)` when simplified reduces to:A. A prime numberB. an irrational numberC. a real which is less than `log_(3)pi`D. a real which is greater than `log_(7)6` |
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Answer» Correct Answer - C::D `N=(1+2log_(3)2)/((1+2log_(3)2)^(2))+(log_(6)2)^(2)` `log_(6)2=(1)/(log_(2)6)=(1)/(log_(2)2+log_(2)3)=(1)/(1+log_(2)3)` let `log_(3)2=t` `impliesN=(1+2t)/((1+t)^(2))+(1)/((1+(1)/(t))^(2))[becauselog_(2)^(3)=(1)/(log_(3)2)]` `N=(1+2t)/((1+t)^(2))+(t^(2))/((1+t)^(2))=1` |
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