Question 1143776
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<pre>
(A)  36 = 4*9 = {{{2^2*3^2}}}.


     Therefore,  {{{log(b,(36))}}} = {{{log(b,(4*9))}}} = {{{log(b,(4))}}} + {{{log(b,(9))}}} = {{{log(b,(2^2))}}} + {{{log(b,(3^2))}}} = {{{2*log(b,(2))}}} + {{{2*log(b,(3))}}} = 2x + 2y.     <U>ANSWER</U>




(B)  432 = 16*27 = {{{2^4*3^3}}}.


     Therefore,  {{{log(b,(432))}}} = {{{log(b,(16*27))}}} = {{{log(b,(16))}}} + {{{log(b,(27))}}} = {{{log(b,(2^4))}}} + {{{log(b,(3^3))}}} = {{{4*log(b,(2))}}} + {{{3*log(b,(3))}}} = 4x + 3y.     <U>ANSER</U>



(C)  {{{log(b,(3))/log(b,(4))}}} = {{{y/(2x)}}}.      <U>ANSWER</U>
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On logarithms and their properties, &nbsp;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, &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.