<PRE><B>Question 796163</B>
The domain of a log function is all values greater than zero.  The log of a negative number is not real.&lt;P&gt;
In this case, that means {{{5 + 4x -x^2 &gt;= 0}}} or {{{x^2 -4x - 5 &lt;= 0}}}&lt;P&gt;
(x-5)(x+1) &lt; 0&lt;P&gt;
x = 5 and x = -1&lt;P&gt;
Because it&#39;s an inequality, set up intervals based on these roots, and test the equation in these intervals.&lt;P&gt;
-infinity to -1, -1 to 5, and 5 to infinity.  Since the inequality is greater than or =, the solution range will include the roots.  You can plug them into the equation to prove it.&lt;P&gt;

-infinity to -1:  Use -10.  -10^2 -4(-10) -5 = 135 &gt; 0, so this interval is not part of the solution.&lt;P&gt;
-1 to 5:  Use 0.  0 - 0 -5 = -5 &lt; 0, so this interval is part of the solution.&lt;P&gt;
5 to infinity:  Use 10.  10^2 - 4(10) - 5 = 55 &gt; 0, so this interval is not part of the solution.&lt;P&gt;
The domain is -1 &lt;= x &lt;= 5</PRE>