Question 250018
<pre>
solve:
{{{log base x[log base 2(log base 3 of 9)]=2}}}
Unfortunately I do not know how to put this without all the words. But this is a problem on one of my take home tests. I dont understand how to solve because I get {{{3^2=9}}} for the log in the parentheses but now I don't knwo what to do?
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In this problem, x is one of the 3 bases given. So, being a LOG-BASE, x CANNOT be 0, and also, x MUST be GREATER than 1. 

 {{{log base x[log base 2(log base 3 of 9)]=2}}} 
  {{{log (x, (log (2, (log (3, (9)))))) = 2}}}, with x > 1

 {{{log (x, (log (2, highlight((log (3, (9))))))) = 2}}}
         {{{log (x, (log (2, (2)))) = 2}}} ---  {{{log (3, (9)) = log (3, (3^2)) = 2}}}
        {{{log (x, highlight((log (2, (2))))) = 2}}}
                {{{log (x, (1)) = 2}}} ---  {{{log (2, (2)) = 1}}}
                    {{{x^2 = 1}}} ----- Converting to EXPONENTIAL form
               {{{x = 0+- sqrt(1) = 0+- 1}}}

However, as stated above, x MUST be > 1, so <font color = red><font size = 4><b>There are NO SOLUTIONS</font></font></b> to this equation.

The other person is WRONG, as he/she states that the value of x is 1.</pre>