The functions we have are y = log (2) x and 2^y = x
2^y = x
take the log the base 2 of both the sides
log (2)(2^y) = log(2) x
use the relation log a^n = n*log a
=> y * log (2) 2 = log(2) x
log(2) 2 = 1
=> y = log(2) x
This is the same as the other graph we have.
The correct option is option c, are the same graph.
y= log2 x ...........(1)
2^y = x.............(2)
We will apply the logarithm of base 2 to the second equation.
==> log2 2^y = log2 x
==> y*log2 2 = log2 x
==> y= log2 x
Then we conclude that the equation (1) is the same as equation (2).
Then the answer is C - are the same graph.