SOLUTION: Evaluate the expression {{{1/log(1/2,100) + 1/log(2/3,100) + 1/log(3/4, 100)}}} +...+ {{{1/log(99/100, 100)}}}.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Evaluate the expression {{{1/log(1/2,100) + 1/log(2/3,100) + 1/log(3/4, 100)}}} +...+ {{{1/log(99/100, 100)}}}.      Log On


   

Question 1048623: Evaluate the expression

1%2Flog%281%2F2%2C100%29+%2B+1%2Flog%282%2F3%2C100%29+%2B+1%2Flog%283%2F4%2C+100%29 +...+ 1%2Flog%2899%2F100%2C+100%29.
Answer by ikleyn(52782) About Me  (Show Source):
You can put this solution on YOUR website!
.
Evaluate the expression

1%2Flog%281%2F2%2C100%29+%2B+1%2Flog%282%2F3%2C100%29+%2B+1%2Flog%283%2F4%2C+100%29 +...+ 1%2Flog%2899%2F100%2C+100%29.
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  1%2Flog%281%2F2%2C100%29 + 1%2Flog%282%2F3%2C100%29 + 1%2Flog%283%2F4%2C+100%29 + . . . + 1%2Flog%2899%2F100%2C+100%29 = log%28100%2C+%281%2F2%29%29 + log%28100%2C+%282%2F3%29%29 + . . . log%28100%2C+%283%2F4%29%29 +  . . . + log%28100%2C+%2899%2F100%29%29 = 

= log%28100%2C+%281%2F2%29%2A%282%2F3%29%2A%283%2F4%29%2Aellipsis%2A%2899%2F100%29%29 = log%28100%2C+%281%2F100%29%29 = -1.

On properties of logarithms see the lessons
    - WHAT IS the logarithm,
    - Properties of the logarithm,
    - Change of Base Formula for logarithms,
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.