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Can you work out the product of these indices?
Age
14 to 16
Challenge level
Problem
Given that $5^p = 9$, $9^q = 12$, $12^r = 16$, $16^s = 20$ and $20^t = 25$,
what is the value of $pqrst$?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: 2
$5^p = 9$ and $9^q = 12$.
Therefore $(5^p)^q = 12$, that is $5^{pq} = 12$.
Similarly, as $12^r = 16$ then $5^{pqr} = 16$
As $16^s = 20$ then $5^{pqrs} = 20$
As $20^t = 25$ then $5^{pqrst} = 25$.
Therefore $pqrst = 2$.