Question 1048623
.
Evaluate the expression


{{{1/log(1/2,100) + 1/log(2/3,100) + 1/log(3/4, 100)}}} +...+ {{{1/log(99/100, 100)}}}.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
  {{{1/log(1/2,100)}}} + {{{1/log(2/3,100)}}} + {{{1/log(3/4, 100)}}} + . . . + {{{1/log(99/100, 100)}}} = {{{log(100, (1/2))}}} + {{{log(100, (2/3))}}} + . . . {{{log(100, (3/4))}}} +  . . . + {{{log(100, (99/100))}}} = 

= {{{log(100, (1/2)*(2/3)*(3/4)*ellipsis*(99/100))}}} = {{{log(100, (1/100))}}} = -1.
</pre>

On properties of logarithms see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/logarithm/what-is-the-logarithm.lesson>WHAT IS the logarithm</A>, 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/logarithm/Properties-of-the-logarithm.lesson>Properties of the logarithm</A>, 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/logarithm/change-of-base-formula-for-logarithms.lesson>Change of Base Formula for logarithms</A>, 

in this site.


Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.