math question

Test Preparation SAT Preparation
1

<p>If n and k are positive integers and 8^n = 2^k, what is the value of n/k?</p>

<p>A) 1/4
B) 1/3
C) 1/2
D) 3
E) 4</p>

<p>My guess was A.</p>

<p>I just did this:</p>

<p>e^8^n = e^2^k</p>

<p>ne^8 = ke^2</p>

<p>n/k = e^2/e^8</p>

<p>= 1/e^6</p>

<p>This is entirely wrong, of course. How do you do this problem?</p>

2

<p>8^n = 2^k
(2^3)^n = 2^k
2^(3n) = 2^k
2n=k
n/k = 1/2</p>

3

<p>it should be B , by using the simpliest example which is 8^1 = 2^3</p>

4

<p>2^3n = 2^k
3n = k
3n/k = k/k
3n/k = 1
n/k = 1/3</p>

<p>OR use logs:</p>

<p>n * log(8) = k * log(2)
n/k = log(2)/log(8)
n/k = 1/3</p>