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

Expert Answers
justaguide eNotes educator| Certified Educator

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.

hala718 eNotes educator| Certified Educator

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.