The sum can be expressed in the form where b and n are positive integers, and b is as small as possible. Find b + n.
log 4 11 + log 8 11 + log 64 11
Using the change of base theorem we have
log 11 log 11 log 11
_____ + ________ + _______ =
log 4 log 8 log 64
log 11 log 11 log 11
_______ + ________ + _______ =
log 2^2 log 2^3 log 2^6
log 11 log 11 log 11
______ + _______ + ________ =
2 log 2 3 log 2 6 log 2
( 1/2 + 1/3 + 1/6) log 11 / log 2 =
( 3/6 + 2/6 + 1/6) log 11 / log 2 =
1 * log 11 / log 2 =
log 11/ log 2 =
log 2 11
b = 2 n = 11
b + n = 13