If log10* + logv=3 and log-logo=1 then find the value of and y
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We know:
1=1
2
1+3=4=2
2
1+3+5=9=3
2
1+3+5+7=16=4
2
....
1+3+5+7+...+13=49=7
2
1+3+5+7+...+13+15=64=8
2
1+3+5+7+...+13+15+17=81=9
2
1+3+5+7+...+13+15+17+19=100=10
2
Replacing the value in the equation, we get:
∴[log(1
2
)+log(2
2
)+...+log(8
2
)+log(9
2
)+log(10
2
)]−[log(1
2
)+log(2
2
)+...+log(7
2
)]=p+qa+rb
⇒log(8
2
)+log(9
2
)+log(10
2
)=p+qa+rb
⇒log(2
6
)+log(3
4
)+2log(2)+2log(5)=p+qa+rb
⇒6log(2)+4log(3)+2log(2)+2log(5)=p+qa+rb
⇒2log(5)+8a+4b=p+qa+rb
∴p=2log(5),q=8,r=4
∴p+2q+3r
=2log(5)+2×8+3×4
=29.397
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