Q.
The value of x in the expression (x+x1og10 x)5 if the third term in the expansion is 10,00,000 is /are
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a
10
b
100
c
10−5/2
d
10−3/2
answer is A.
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Detailed Solution
Inclusion of logx implies x>0 . Now 3rd term in the expansion is T2+1=5C2x5−2(x1og10x)2=1000000 (given)Or x3+2log10x=105 Taking logarithm of both sides we get(3+2log10x)log10x=5 or2y2+3y−5=0 where log10x=y or(y−1)(2y+5)=0 ory=1 or−5/2 orlog10x=1 or −5/2 ∴ x=101=10 or10−5/2
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