the graphs of y=log[2]x and 2^y=x :

a intersect in only one point

b intersect in two points

c are the same graph

d do not intersect at all

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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.**

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.**

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