<PRE><B>Question 1144036</B>
.
&lt;pre&gt;

{{{33/25}}} = {{{(3*11)/25}}} = {{{(3*4*11)/(4*25)}}}    &lt;&lt;&lt;---=== I multiplied the numerator and denominator 
                                  by the factor 4, without changing the fraction.

                                  So, I can continue the chain of equalities:


{{{33/25}}} = {{{(3*11)/25}}} = {{{(3*4*11)/(4*25)}}} = {{{(12*11)/10^2}}}.


Therefore,


{{{log(7,(33/25))}}} = {{{log(7,((12*11)/10^2))}}} = apply the logarithm properties = {{{log(7,(12))}}} + {{{log(7,(11))}}} - {{{2*log(7,(10))}}} = Y + Z - 2X.    &lt;U&gt;ANSWER&lt;/U&gt;
&lt;/pre&gt;

Answered, &amp;nbsp;explained, &amp;nbsp;solved and completed.


---------------------


On logarithms and their properties, &amp;nbsp;see the lessons

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/logarithm/what-is-the-logarithm.lesson&gt;WHAT IS the logarithm&lt;/A&gt; 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/logarithm/Properties-of-the-logarithm.lesson&gt;Properties of the logarithm&lt;/A&gt; 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/logarithm/change-of-base-formula-for-logarithms.lesson&gt;Change of Base Formula for logarithms&lt;/A&gt; 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/logarithm/Evaluate-logarithms-without-using-a-calculator.lesson&gt;Evaluate logarithms without using a calculator&lt;/A&gt; (*)

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/logarithm/Proving-equalities-with-logarithms.lesson&gt;Proving equalities with logarithms&lt;/A&gt; 

in this site.


Especially, &amp;nbsp;look into the lesson &amp;nbsp;(*) &amp;nbsp;and find there very similar solved problems.


Also, &amp;nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson&gt;ALGEBRA-I - YOUR ONLINE TEXTBOOK&lt;/A&gt;.


The referred lessons are the part of this online textbook under the topic &quot;&lt;U&gt;Logarithms&lt;/U&gt;&quot;.



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.


</PRE>