Question 1206837
<pre>

{{{3^x=x^9}}}

If in an equation to solve, the variable to solve for appears both as an
exponent and a non-exponent, as it does here, then there is no way to solve for
the variable other than by iterative methods.  

Iterative methods are trial and error processes.  
Try a number. If it's too big, try a smaller number.
If it's too small try a bigger number.
Always try a number between the last number you tried that was too big, and
the last number you tried that was too small. 
Eventually you will have the solution trapped between two numbers, that get
closer and closer together.

That's a very time-consuming process, but technology can do that trial and 
error process instantaneously.

On a TI-84 Plus CE calculator you can get x = 1.1508248, an approximate solution
trapped between 1.15082475 and 1.15082485.

Edwin</pre>