Question 1210272
<pre>
{{{(-9x + 57)^x = 729}}}

When the unknown in an equation appears as an exponent as well as a term or
factor, there is no way to solve it but by trial and error or some iterative
method which amounts to trial and error.

Since 729 = 3<sup>6</sup>, you might try 6:

{{{(-9(6) + 57)^6 = 729=3^6}}}

{{{(-54+57)^6 = 3^6}}}

{{{(-3)^6 = 3^6}}}

So 6 is a solution.

With a graphing calculator, you can also get another solution, although
this one is approximate:

x = 1.7746996

{{{drawing(400,400,-1,7,0,400000, graph(400,400,-1,7,0,400000,729,(-9x+57)^x),
graph(400,400,-1,7)), locate(-1,0,0))
}}}
       {{{graph(350,10,0,7,-400,3)}}}


Edwin</pre>