SOLUTION: Good morning can you explain me why : 2^log2(x) = 8 gives as result x = 8 ?? Many Thanks

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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