What is (log3 x)^2=log3 (x^2) + 3 ?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

(log3 x)^2=log3 (x^2) + 3

First we know that log a^b = b*log a

==> (log3 x)62 = 2log3 x + 3

Now, we will move all terms to the left side so the right side is 0:

==>( log3 x)^2 - 2log3 x - 3 = 0

Now let us...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

(log3 x)^2=log3 (x^2) + 3

First we know that log a^b = b*log a

==> (log3 x)62 = 2log3 x + 3

Now, we will move all terms to the left side so the right side is 0:

==>( log3 x)^2 - 2log3 x - 3 = 0

Now let us assume that:

log3 x = y

==? y^2 - 2y - 3 = 0

Now we will factor:

( y-3)(y+1) = 0

==> y1= 3  ==> log3 x = 3 ==> x = 3^3 = 27

==> y2= -1 ==> log3 x = -1 ==> x = 3^-1 = 1/3

Then the answer is:

x = { 1/3 , 27}

Approved by eNotes Editorial Team