7153
/www/nrich/html/content/id/7153/
1
2011-02-01T00:00:01
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<p>Let $a= 2^{25}$, $b= 8^8$ and $c= 3^{11}$.<br></br>
<br></br>
Now order the letters so that we get ${?}&lt; {?}&lt; {?}$<br></br>
<br></br>
<br></br>
If you liked this problem, <a href="http://nrich.maths.org/6401&part=">here is an NRICH task</a> which challenges you to use similar mathematical ideas.<br></br>
<br></br>
</p></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
By comparing <span style="font-style: italic;">b</span> and <span style="font-style: italic;">c</span> first, we have $b= 8^8=
(2^3)^8=2^{24}=(2^2)^{12}=4^{12}> 3^{11} = c$<br></br>
<br></br>
so $c< b$.<br></br>
<br></br>
But also $b= 2^{24}< 2^{25}=a$ so $b< a$.<br></br>
<br></br>
Together these give $c< b< a$.<br></br>
<br></br>
<br></br></mdoxml>
2
3
0
0
1
1
0
Weekly Problem 6 - 2011
Weekly Problem 6 - 2011
Numbers and the Number System
Powers & roots
Algebra
Inequality/inequalities
Algebra
Using symbols