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

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Math Expert
Joined: 02 Sep 2009
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If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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13 Mar 2015, 07:53
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82% (01:47) correct 18% (01:40) wrong based on 122 sessions

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

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

Kudos for a correct solution.

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Re: If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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13 Mar 2015, 08:19
1
Bunuel wrote:
If N = 2^0.15 and N^b = 16, b must equal

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

Kudos for a correct solution.

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
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Lucky

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Re: If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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13 Mar 2015, 09:21
15/100 = 3/20
N = 2 ^ 3/20

N^b = 2^4

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

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Re: If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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13 Mar 2015, 09:26
1
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.
Math Expert
Joined: 02 Sep 2009
Posts: 49965
Re: If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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15 Mar 2015, 22:56
Bunuel wrote:
If N = 2^0.15 and N^b = 16, b must equal

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

Kudos for a correct solution.

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.

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Re: If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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17 Mar 2015, 03:23
$$N = 2^{0.15}$$

$$n^b = 2^{0.15b}$$

Given that $$n^b = 16 = 2^4$$

Bases are same, equating powers

0.15b = 4

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

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Re: If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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12 Apr 2015, 09:26
Bunuel wrote:
Bunuel wrote:
If N = 2^0.15 and N^b = 16, b must equal

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

Kudos for a correct solution.

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.

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 ?
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Re: If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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12 Apr 2015, 11:04
2^0.15b = 2^4, by substituting N - 2^0.15in the second Equation. Therefore, 0.15 b = 4, b = 80/3
Math Expert
Joined: 02 Sep 2009
Posts: 49965
Re: If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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14 Apr 2015, 05:43
LaxAvenger wrote:
Bunuel wrote:
Bunuel wrote:
If N = 2^0.15 and N^b = 16, b must equal

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

Kudos for a correct solution.

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.

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 ?

(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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Re: If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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22 Sep 2018, 02:21
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Re: If N = 2^0.15 and N^b = 16, b must equal &nbs [#permalink] 22 Sep 2018, 02:21
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# If N = 2^0.15 and N^b = 16, b must equal

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