Question

Sum of 10 terms of the progression log2+log4+log8+log16+....................is

Answer 1

log2+log4+log8+log16+log32+log64+log128+log256+log512+log1024

Answer 2

The sum of 10 terms of the progression is 55log(2).

Step-by-step explanation:

The given progression is

$\log 2+\log 4+\log 8+\log 16+...$

We need to find the sum of 10 terms of the progression.

The given progression can be rewritten as

$\log 2^1+\log 2^2+\log 2^3+\log 2^4+...$

So, the sum of first 10 terms is

$\log 2^1+\log 2^2+\log 2^3+\log 2^4+...+\log 2^{10}$

Using the property of logarithm we get

$1\log 2+2\log 2+3\log 2+4\log 2+...+10\log 2$        $[\because \log x^a=a\log x]$

Taking log 2 common.

$\log 2(1+2+3+4+5+6+7+8+9+10)$

$\log 2(55)$

$55\log 2$

Therefore, the sum of 10 terms of the progression is 55log(2).

#Learn more

The sum of 20 terms of log2+log4+log8+..... is: a) 20log2 b) log20 c) 210log2 d) log2.

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