how the heck do you solve this?

log_3(3/4+4/5+5/6+6/7+7/8+8/9) divided by log_10(4/5+5/6+6/7+7/8+8/9+9/10)

 

=2.05815630.... I have assumed that log_3 means "Log(base 3)",

You add all the fractions inside the bracket...3/4+4/5+5/6.......=5.004365........, then

Log(5.004365)/Log(3) =1.465768....................(1), then,

You add all the fractions in the 2nd part....4/5+5/6+6/7...........=5.154365....., then take the log of this: Log(5.154365) =0.712175................(2),

Divide the result in (1) by the result in (2) and you get:

1.465768/.712175 =2.0581563, which is the final answer.