Question 1209572
<pre>

That's a clever way for it avoids logarithms. But I think this student is
studying solving exponential equations by taking natural logs of both sides.  
So I think the student would do it this way:

{{{matrix(7,1,
2^a=3,"",
ln(2^a)=ln(3),"",
a*ln(2)=ln(3),"",
a=ln(3)/ln(2))}}}       {{{matrix(7,1,
3^b=2,"",
ln(3^b)=ln(2),"",
b*ln(3)=ln(2),"",
b=ln(2)/ln(3))}}}       {{{matrix(9,2,
1/(a+1)+1/(b+1),""="",
"","",

1/   ( ln(3)/ln(2) + 1) + 1/   ( ln(2)/ln(3) + 1),""="",
"","",

ln(2)/(ln(3)+ln(2)) + ln(3)/(ln(2)+ln(3)),""="",
"","",

(ln(2)+ln(3))/(ln(3)+ln(2)),""="",
"","",

1,"")}}}   

Edwin</pre>