Question 1131: HOw do I solve log16 2=w
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! 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.
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