log 既問題

log 49 to base 2 = log 49/log 2 both to base 10.
log 16 to base 3 = log 16/log 3 both to base 10
log 27 to base 7 = log 27/ log 7 both to base 10.
log 49 = log 7^2 = 2 log 7.
log 16 = log 2^4 = 4 log 2.
log 27 = log 3^3 = 3 log 3.
so it becomes
2 log 7/log 2 x 4 log 2/log 3 x 3 log 3/log 7
= 2 x 4 x 3 = 24.



2009-04-02 22:32:47 補充：
This question is based on 2 principles : (1)log A to the base B = log A/ log B both to a same base C. (2) log (M^n) = n log M.