Match the following Column I to Column II

Explanation

(A) `log_(3)(5+8log_(49)(5+4log_(7)49))=k`
`implieslog _(3)(5+8 log_(49)7)=k`
`implieslog_(3)9=k impliesk=2`
`therefore(k^(2)+1)=(2^(2))+1=5.`
(B) We have `sqrt(9+sqrt(77))=ximpliesx^(2)=9+sqrt77.....(1)`
As, `(9+sqrt77)(9-sqrt77)=4implies(9-sqrt77)=(4)/(x^(2)).......(2)`
`impliesx^(2)+(4)/(x^(2))=10implies(x+(2)/(x))^(2)-4=18implies(x+(2)/(x))^(2)=22`
`implies((x+(2)/(x))^(2))/(11)=(22)/(11)2.`
(C ) `sin^(2)theta+2cos(theta+phi)[cos (theta-phi)=-cos(theta+phi)]+2cos^(2)(theta+phi)-1 =2sin^(2)theta+2(cos^(2)theta-sin^(2)phi)-1`
`=1-2sin^(2)phi=cos2 phi=-1=b`
` a+b=0`
(D) `log_(e)2.log_(b)625=log_(10)16.log_(e)10`
`implies(log2)/(loge)xx(log625)/(logb)-(log_(10)16)/(log10)xx(log10)/(loge)`
`implies((log2)(4 log5))/(logb)=4(log2)`
`implieslog b =log5 b=5`