Find the value of log_8 9 times log_9 10 xx * times log_n(n+1) * log_(n+1)8

Emmanuel Giles

Emmanuel Giles

Answered question

2022-11-10

Find the value of log 8 9 × log 9 10 × × log n ( n + 1 ) × log n + 1 8
I'm completely stumped as to where to even begin looking. If someone could point me in the right direction I'd appreciate it.

Answer & Explanation

Stella Andrade

Stella Andrade

Beginner2022-11-11Added 19 answers

Remember that log a b = ln b ln a . The product then telescopes.
Nola Aguilar

Nola Aguilar

Beginner2022-11-12Added 4 answers

Rewrite them as
log ( 9 ) log ( 8 ) log ( 10 ) log ( 9 ) log ( 11 ) log ( 10 ) log ( 12 ) log ( 11 ) log ( n + 1 ) log ( n ) log ( 8 ) log ( n + 1 ) = 1 ,
since all of the logs cancel in-between and that leaves the two log ( 8 ) 's on either side in the denominator and numerator.

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