+4622 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?
+26387 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?
\(\begin{array}{|rcll|} \hline 197_{10} &=& 11000101_2 \\ 197_{10} &=& 21022_3 \\ 197_{10} &=& 3011_{\color{red}4} \\ 197_{10} &=& 1242_{\color{red}5} \\ 197_{10} &=& 525_6 \\ 197_{10} &=& 401_7 \\ 197_{10} &=& 305_8 \\ 197_{10} &=& 238_9 \\ 197_{10} &=& 197_{10} \\ \cdots \\ \hline \end{array}\)
b is 4 or 5
+26387 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?
\(\begin{array}{|rcll|} \hline 197_{10} &=& 11000101_2 \\ 197_{10} &=& 21022_3 \\ 197_{10} &=& 3011_{\color{red}4} \\ 197_{10} &=& 1242_{\color{red}5} \\ 197_{10} &=& 525_6 \\ 197_{10} &=& 401_7 \\ 197_{10} &=& 305_8 \\ 197_{10} &=& 238_9 \\ 197_{10} &=& 197_{10} \\ \cdots \\ \hline \end{array}\)
b is 4 or 5
