If N = 2^0.15 and N^b = 16, b must equal

Question

A. 3/80
B. 3/5
C. 4
D. 5/3 
E. 80/3

Lucky2783 · Answer

N = 2^0.15 and N^b = 16
so 
 2^(^(^1^5^/^1^0^0^)^*^b^)= 2^4 
 (15/100) * b = 4 
 b = 80/3

on a different note , is there an easy way to write the exponents , square roots , less than , subscripts (X1,X2 etc.)?
thanks
lucky

peachfuzz · Answer

15/100 = 3/20
N = 2 ^ 3/20

N^b = 2^4

(2^3/20)^b = 2^4
b = 80/3

Answer: E

mvictor · Answer

If N = 2^0.15 and N^b = 16, b must equal

we can rewrite this as

(2^0.15)^b = 16
2^0.15b = 2^4
and 0.15b = 4
we can rewrite this as:
b= 4/0.15 = 400/15
this is definitely more than answer choices A,B,C,D.

hence, the only possible answer is E.

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

First, we have to express 0.15 as a fraction: 0.15 = 3/20.

Also, 16 is 2 to the power of 4, so the equation with b tells us:  (2^{\frac{3}{20}})^b=2^4

Bases are the same, so we can equate the exponents.

3/20*b = 4 --> b = 80/3.

Answer = (E).

PareshGmat · Answer

N = 2^{0.15}

n^b = 2^{0.15b}

Given that  n^b = 16 = 2^4

Bases are same, equating powers

0.15b = 4

b = \frac{400}{15} = \frac{80}{3}

Answer = E

LaxAvenger · Answer

should the equation not be (2^3/20)^b = 2^4

giving us 3/20^b = 4

why are we saying 3/20 * b = 4 ?

nphatak · Answer

2^0.15b = 2^4, by substituting N - 2^0.15in the second Equation. Therefore, 0.15 b = 4, b = 80/3

Bunuel · Answer

(2^3/20)^b = 2^(3/20*b), so we have that 2^(3/20*b) = 2^4 --> 3/20*b = 4. Theory on Exponents: math-number-theory-88376.html Tips on Exponents: exponents-and-roots-on-the-gmat-tips-and-hints-174993.html All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39 All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60 Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

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If N = 2^0.15 and N^b = 16, b must equal

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