Question 1131
By definition of logarithm,log16 2= w means 16^w = 2,
 since 16 = 2^4, so (2^4)^w = 2.
 By exponential law ,(2^4)^w = 2^(4w) = 2 = 2^1.
 Comparing the exponent, we have 4w = 1, w = 1/4.

 Another way,use the rule of changing base (to base c)
 loga b = logc b/logc a.
 
 w = log16 2 = log2 2/ log2 16 (changing base from 16 to 2)
         = 1 / log2 2^4
         = 1 / (4 log2 2)
         = 1/4 (same answer)


 I prefer to use the 2nd method.