+0  
 
0
82
1
avatar+1148 

Suppose that \(b\)  is a positive integer greater than or equal to 2. When 197 is converted to base \(b\) , the resulting representation has 4 digits. What is the number of possible values for b?

tertre  Mar 15, 2017

Best Answer 

 #1
avatar+18354 
+10

Suppose that is a positive integer greater than or equal to 2. 

When 197 is converted to base b, the resulting representation has 4 digits.

What is the number of possible values for b?

 

\(\begin{array}{|rcll|} \hline 197_{10} &=& 11000101_2 \\ 197_{10} &=& 21022_3 \\ 197_{10} &=& 3011_{\color{red}4} \\ 197_{10} &=& 1242_{\color{red}5} \\ 197_{10} &=& 525_6 \\ 197_{10} &=& 401_7 \\ 197_{10} &=& 305_8 \\ 197_{10} &=& 238_9 \\ 197_{10} &=& 197_{10} \\ \cdots \\ \hline \end{array}\)

 

b is 4 or 5

 

laugh

heureka  Mar 15, 2017
Sort: 

1+0 Answers

 #1
avatar+18354 
+10
Best Answer

Suppose that is a positive integer greater than or equal to 2. 

When 197 is converted to base b, the resulting representation has 4 digits.

What is the number of possible values for b?

 

\(\begin{array}{|rcll|} \hline 197_{10} &=& 11000101_2 \\ 197_{10} &=& 21022_3 \\ 197_{10} &=& 3011_{\color{red}4} \\ 197_{10} &=& 1242_{\color{red}5} \\ 197_{10} &=& 525_6 \\ 197_{10} &=& 401_7 \\ 197_{10} &=& 305_8 \\ 197_{10} &=& 238_9 \\ 197_{10} &=& 197_{10} \\ \cdots \\ \hline \end{array}\)

 

b is 4 or 5

 

laugh

heureka  Mar 15, 2017

5 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details