# recurrence

• Feb 1st 2009, 08:23 AM
qwerty321
recurrence
HEllo
Can someone guide me with this?

Consider the recurrence relation :
an = (a(n-1))^3 * a(n-2)^2
Use logarithms to change (1) into a linear recurrence relation for (
bn =

log
2(an)). Find such recurrence relation for {bn}

Thank you
• Feb 1st 2009, 11:53 PM
Constatine11
Quote:

Originally Posted by qwerty321
HEllo

Can someone guide me with this?

Consider the recurrence relation : an = (a(n-1))^3 * a(n-2)^2
Use logarithms to change (1) into a linear recurrence relation for (bn =
log2(an)). Find such recurrence relation for {bn}

Thank you

$a_n=a_{n-1}^3 \times a_{n-2}^2$

take logs (to base 2):

$\log_2(a_n)=3\log_2(a_{n-1})+2 \log_2(a_{n-2})$

putting $b_n=\log_2(a_n)$ this becomes:

$
b_n=3b_{n-1}+2b_{n-2}
$

.