If x= 2^b - (8^8 + 8^6), for which of the following b values

Question

If x= 2^b - (8^8 + 8^6), for which of the following b values is x closest to 0?

(A) 20
(B) 24
(C) 25
(D) 30
(E) 42

Bunuel · Accepted Answer

8^8 + 8^6=8^2*8^6 + 8^6=64*8^6+8^6=65*8^6=65*2^{18}\approx{2^{6}*2^{18}}=2^{24} .

2^b - (8^8 + 8^6)=0  -->  2^b - 2^{24}=0  -->  b=24

Answer: B.

OR:  8^8 + 8^6 is very close to 8^8=2^24, thus b=24.

mikemcgarry · Answer

Dear abhisheksharma85 , I'm happy to help with this. :-)

Recall the exponent rule: (a^m)^n = a^(m*n) Therefore, 8^8 + 8^6 = (2^3)^8 + (2^3)^6 = 2^24 + 2^18 This is the thing we want to cancel with 2^b. Well, keep in mind that 2^24 is 2^6 = 64 times larger than 2^18, so for the purposes of cancelling, we will ignore the tinier number. If we want to cancel the 2^24, we need b = 24, answer = (B) . Does all this make sense? Mike :-)

Bunuel · Answer

Similar questions to practice: the-value-of-10-8-10-2-10-7-10-3-is-closest-to-which-of-95082.html which-of-the-following-is-closest-to-10180-1030-a-110224.html which-of-the-following-best-approximates-the-value-of-q-if-99674.html new-tough-and-tricky-exponents-and-roots-questions-125956-40.html if-x-10-10-x-2-2x-7-3x-2-10x-2-is-closest-to-143897.html 1-0-0001-0-04-10-the-value-of-the-expression-above-is-59398.html m24-q-7-explanation-76513.html 10-180-10-30-which-of-the-following-best-approximates-84309.html Hope it helps.

PareshGmat · Answer

8^8 = 2^24
8^6 = 2^18

2^24 + 2^18 is nearly to 2^24, so b=24 = Answer = B

sashiim20 · Answer

x= 2^b - (8^8 + 8^6)

8^8 + 8^6 = 8^6(8^2+1)

We can approximate the value.  1  is very small value compared to  8^2  hence we can ignore  1 . Therefore we get;

8^8 + 8^6 = 8^6(8^2) = 8^{(6+2)} = 8^8 = (2^3)^{8} = 2^ {(3*8)} = 2^{24}

x= 2^b - 2^{24}

For " x " to be closest to  0 , value of " b " should be  = 24

Answer (B)...

Nisha0987 · Answer

2^24 + 2^18 is nearly to 2^24, so b=24 
Why are we ignoring 2^18 here? Can someone explain this to me?

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If x= 2^b - (8^8 + 8^6), for which of the following b values

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If x= 2^b - (8^8 + 8^6), for which of the following b values

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