If log 21 / 2 a+ log 21 / 4 a+ log 21 / 6 a+ log 21 / 8 a+ ldots. upto 20 terms is 840 , then a equal to

Question

If log 21 / 2 a+ log 21 / 4 a+ log 21 / 6 a+ log 21 / 8 a+ ldots. upto 20 terms is 840 , then a equal to (A) 2 (B) 1 (C) 4 (D) √2

Tardigrade Admin · Accepted Answer

=2 log 2 a +4 log 2 a +6 log 2 a + ldots ldots ldots ldots+40 log 2 a = log 2 a 2+4+ ldots ldots+40 =(20/2)(2+40) log 2 text a =420 log 2 a =840 ⇒ log 2 a =2 ⇒ a=4

Q. If $lo g_{2^{1/2}} a + lo g_{2^{1/4}} a + lo g_{2^{1/6}} a + lo g_{2^{1/8}} a + \dots$ . upto 20 terms is 840 , then a equal to

2

1

4

$2$

$= 2 lo g_{2} a + 4 lo g_{2} a + 6 lo g_{2} a + \dots\dots\dots\dots + 40 lo g_{2} a$
$= lo g_{2} a {2 + 4 + \dots\dots + 40}$
$= \frac{20}{2} (2 + 40) lo g_{2} a$
$= 420 lo g_{2} a = 840$
$\Rightarrow lo g_{2} a = 2$
$\Rightarrow a = 4$

Q. If log21/2​a+log21/4​a+log21/6​a+log21/8​a+…. upto 20 terms is 840 , then a equal to

2

1

4

2​

=2log2​a+4log2​a+6log2​a+…………+40log2​a =log2​a{2+4+……+40} =220​(2+40)log2​ a =420log2​a=840 ⇒log2​a=2 ⇒a=4

Q. If $lo g_{2^{1/2}} a + lo g_{2^{1/4}} a + lo g_{2^{1/6}} a + lo g_{2^{1/8}} a + \dots$ . upto 20 terms is 840 , then a equal to

$2$

$= 2 lo g_{2} a + 4 lo g_{2} a + 6 lo g_{2} a + \dots\dots\dots\dots + 40 lo g_{2} a$
$= lo g_{2} a {2 + 4 + \dots\dots + 40}$
$= \frac{20}{2} (2 + 40) lo g_{2} a$
$= 420 lo g_{2} a = 840$
$\Rightarrow lo g_{2} a = 2$
$\Rightarrow a = 4$