Question 1004547
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.