Question 1004547: Good morning can you explain me why : 2^log2(x) = 8 gives as result x = 8 ??
Many Thanks
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! this follows from the basic definition of logs.
the basic definition of logs says:
logb(c) = d if and only if b^d = c
the reverse is also true.
b^d = c if and only if logb(c) = d
we'll start with b^d = c
we know that, by the basic definition of logs, b^d = c if and only if logb(c) = d
if we let:
b = 2
d = log2(x)
c = 8
then we get:
b^d = c if and only if logb(c) = d becomes:
2^(log2(x)) = 8 if and only if log2(8) = log2(x)
this is true if and only if x = 8.
this is a direct result of the application of the basic definition of logs.
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