Question 1096787
<pre>
{{{

(log(3,(3/4))+log(3,(4/5))+log(3,(5/6))+log(3,(6/7))+log(3,(7/8))+log(3,(8/9)) )/

(log((4/5))+log((5/6))+log((6/7))+log((7/8))+log((8/9))+log((9/10))){{{""=""}}}



Use the fact that the sum of logs equals the log of the product
of what the logs are taken of:

{{{log(3,(  (3/4)(4/5)(5/6)(6/7)(7/8)(8/9)^""  )) /

log( ((4/5)(5/6)(6/7)(7/8)(8/9)(9/10)^"") )  


}}}

Cancel what will cancel:

{{{log(3,(  (3/cross(4))(cross(4)/cross(5))(cross(5)/cross(6))(cross(6)/cross(7))(cross(7)/cross(8))(cross(8)/9)^""  )) /

log( ((4/cross(5))(cross(5)/cross(6))(cross(6)/cross(7))(cross(7)/cross(8))(cross(8)/cross(9))(cross(9)/10)^"") )}}}{{{""=""}}}

{{{log(3,(3/9))/log((4/10))}}}{{{""=""}}}

{{{log(3,(1/3))/log((4/10))}}}{{{""=""}}}

{{{log(3,(3^(-1)))/log((4/10))}}}{{{""=""}}} 

{{{((-1)log(3,(3)))/(log((4))-log((10)))}}}{{{""=""}}}

{{{((-1)(1))/(log((4))-1)}}}{{{""=""}}}

{{{(-1)/(log((4))-1)}}}{{{""=""}}}

Multiply top and bottom by -1:

{{{1/(-log((4))+1)}}}{{{""=""}}}

{{{1/(1-log((4)))}}}



Edwin</pre>