Question

2^2008-2^2007-2^2006-2^2005=k*2^2005 find value of k

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Answer 1

Answer:

The value of k is 1

Step-by-step explanation:

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Answer 2

$\sf {2}^{2008} - {2}^{2007} - {2}^{2006} - {2}^{2005} = k \times {2}^{2005}$ value of k = 1

Given : $\sf {2}^{2008} - {2}^{2007} - {2}^{2006} - {2}^{2005} = k \times {2}^{2005}$

To find : The value of k

Solution :

Step 1 of 2 :

Write down the given equation

The given equation is

$\sf {2}^{2008} - {2}^{2007} - {2}^{2006} - {2}^{2005} = k \times {2}^{2005}$

Step 2 of 2 :

Find the value of k

$\sf {2}^{2008} - {2}^{2007} - {2}^{2006} - {2}^{2005} = k \times {2}^{2005}$

$\sf \implies \: {2}^{3} .{2}^{2005} - {2}^{2} .{2}^{2005} -2. {2}^{2005} - {2}^{2005} = k \times {2}^{2005}$

$\sf \implies \: 8.{2}^{2005} - 4.{2}^{2005} -2. {2}^{2005} - {2}^{2005} = k \times {2}^{2005}$

$\sf \implies \: (8 - 4 - 2 - 1){2}^{2005} = k \times {2}^{2005}$

$\sf \implies \: {2}^{2005} = k \times {2}^{2005}$

$\sf \implies \: k \times {2}^{2005} = {2}^{2005}$

$\sf \implies \: k = 1$

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