Question 825914
<pre>
{{{log(5,(25sqrt(125)))}}}

{{{log(5,(5^2*sqrt(5^3)))}}}

{{{log(5,(5^2*(5^3)^(1/2)))}}}

{{{matrix(2,1,"",log(5,(5^2*5^(3/2))))}}}

{{{matrix(2,1,"",log(5,(5^(2+3/2))))}}}


{{{matrix(2,1,"",log(5,(5^(4/2+3/2))))}}}

{{{matrix(2,1,"",log(5,(5^(7/2))))}}}

That expression asks "To what power must I raise {{{5}}} to get {{{matrix(2,1,"",5^(7/2))}}}?
Answer:  "I must raise {{{5}}} to the {{{7/2}}} power to get  {{{matrix(2,1,"",5^(7/2))}}}, of course!
 
Therefore the answer to the problem is

       {{{7/2}}}

Edwin</pre>