Is 2^x greater than 100?

Question

(1)  2^{\sqrt{x}}=8

(2)  \frac{1}{2^x} < 0.01

maheshaero20 · Answer

1. on solving x=9. Therefore 2^9 >100 (SUFFICIENT)
2. Inverse the equation; we get 2^x>100 (SUFFICIENT)

Ans: D

EatMyDosa · Answer

Let's rephrase the question: Is 2^x > 100? Now, we know that 2^6 = 64 and 2^7 = 128 Therefore, 2^x >100 for any integer value of x>6. So, in other words, the question is asking if x >6? Statement 1: 2^(x/2) = 2^3 i.e. x/2 = 3 x = 6 Since x is NOT greater than 6, so this statement is SUFFICIENT ---- eliminate B, C, E Statement 2: 1/2^x < 1/100 Since the terms on both sides are POSITIVE, we can cross multiply without changing the Inequality sign 100 < 2^x ---- this is possible only when x>6 So, this statement is also SUFFICIENT ----eliminate A Correct Answer - D (both statements are individually SUFFICIENT to answer the question)

revamoghe · Answer

Please help with the 2nd equation?  Bunuel

Bunuel · Answer

\frac{1}{2^x} < 0.01 ;

\frac{1}{2^x} < \frac{1}{100} ;

Cross multiply:  100<2^x .

ag153 · Answer

Bunuel  pls help with statement 1. I cannot figure out how to equate the exponents since we are not told anything about x being an integer. Also do not know if it is 6 or 9.

ChrisJ · Answer

x = 9
2 power (root x)= 8, 
Therefore; root x =3
x =9

Posted from my mobile device

Bunuel · Answer

2^{\sqrt{x}}=8 ;

2^{\sqrt{x}}=2^3 ;

\sqrt{x}=3 ;

x=3^2=9 .

Hope it's clear.

Elite097 · Answer

Bunuel  Pls unblock ag153. In the middle of their prep how can you bock people for random reasons like people giving kudos that too without any warning??

Also I have the same doubt as ag153. I want to know that we are not told exponent is an integer so how can we equate the 2 sides?

Cav · Answer

In statement (2), how can we cross-multiply if we do not know the sign of 'x'?

My understanding is that we cannot multiply or divide by something in an inequality if we do not know its sign.  Bunuel  Can you please clarify?

Bunuel · Answer

Yes, but the point is that 2^x is always positive, so it's safe to cross-multiply.

bumpbot · Answer

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Is 2^x greater than 100?

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