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the graphs of y=log[2]x and 2^y=x :a   intersect in only one point b   intersect...

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mandabearbaybe | Student, Grade 10 | eNotes Newbie

Posted March 22, 2011 at 4:01 AM via web

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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

2 Answers | Add Yours

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted March 22, 2011 at 4:06 AM (Answer #1)

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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.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 22, 2011 at 4:15 AM (Answer #2)

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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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