Question 1097315
.
<pre>
{{{n^2+m^2}}} = 11nm   is equivalent to  

{{{n^2- 2mn + m^2}}} = 9nm   is equivalent to  

{{{(n-m)^2}}} = 9nm   is equivalent to  

{{{((n-m)^2)/9}}} = nm   is equivalent to  

{{{((n-m)/3)^2}}} = nm.



Under the assumption  n > 0,  m > 0,  n > m  it implies that


2*log((n-m)/3) = log(n) + log(m),    which is equivalent to


(1/2)*(log(n) + log(m)) = log((n-m)/3).
</pre>

QED.



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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>".



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I

https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.