Question 1089581
.
<pre>
  {{{log(2,(3))*log(3,(4))*log(4,(5))* . . . *log(1023,(1024))}}} = 


         Use the base change formula  {{{log(a,(b))}}} = {{{log(b)/log(a)}}} to get


= {{{(log(3)/log(2))*(log(4)/log(3))*(log(5)/log(4))* ellipsis *(log(1024)/log(1023))}}} = (cancel all appropriate factors) = 

= {{{log(1024)/log(2)}}} = (use the base change formula again to get) = {{{log(2,(1024))}}} = 10.
</pre>

Solved.



On logarithms and their properties, 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> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/logarithm/How-to-solve-logarithmic-equations.lesson>Solving logarithmic equations</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/logarithm/Using-logarithms-to-solve-real-world-problems.lesson>Using logarithms to solve real world problems</A> 

in this site.


Also, &nbsp;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>.


The referred lessons are the part of this online textbook under the topic "<U>Logarithms</U>".