SOLUTION: Logx(6x-9)=2

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Question 1200693: Logx(6x-9)=2
Found 4 solutions by Theo, ikleyn, MathTherapy, greenestamps:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
log(6x-9) = 2 if and only if 10^2 = 6x - 9
add 9 to both sides of the equation to get:
109 = 6x
solve for x to get:
x = 109/6.
that's your answer.
to confirm, use your calculator to find log(109/6 - 9).
it will be equal to 2.
Answer by ikleyn(52908)   (Show Source): You can put this solution on YOUR website!
.
Logx(6x-9)=2
~~~~~~~~~~~~~~~~~~


            I believe that your equation is Log(x(6x-9)) = 2.

            The other tutor incorrectly read/interpret the problem and gave incorrect solution/answer.
            See the correct solution below. 


log(x*(6x-9) = 2 means that

    x*(6x-9) = 100.   


Reduce this equation to the standard quadratic equation form

          6x^2 - 9x - 100 = 0.


Solve it using the quadratic formula.  You will get

     =  =  4.9008  (approximately);

     =  = -3.4008  (approximately);

Solved (correctly).



Answer by MathTherapy(10557)   (Show Source): You can put this solution on YOUR website!
If logx(6x - 9) = 2, then x = 3.

The person who responded, TOTALLY omitted the x. Why?
Answer by greenestamps(13215)   (Show Source): You can put this solution on YOUR website!


The format of the given equation is open to different interpretations, so it is inappropriate for one tutor to say another tutor misinterpreted the problem.

To me, the most reasonable interpretation of the given equation is



In that case, as one of the other tutors stated without showing the solution method, use the basic definition of logarithms to change the logarithmic form to exponential form.



The solution method is then the same as for any quadratic equation.






ANSWER: x=3
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