<PRE><B>Question 1113483</B>
.
&lt;pre&gt;
1.  Start from the the deepest logarithm:

    {{{log(2,(8))}}} = 3.    ( &lt;&lt;&lt;---=== no more explanations ! You must know it !)



2.  Now one level up:

    {{{log(3, (log(2,(8))))}}} = {{{log(3,(3))}}} = 1.



3.  Now last step

    {{{log(4, (log(3, (log(2,(8))))))}}} = {{{log(4,(1))}}} = 0.
&lt;/pre&gt;

Solved.


----------------
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=http://www.algebra.com/algebra/homework/logarithm/How-to-solve-logarithmic-equations.lesson&gt;Solving logarithmic equations&lt;/A&gt; 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/logarithm/Using-logarithms-to-solve-real-world-problems.lesson&gt;Using logarithms to solve real world problems&lt;/A&gt; 

in this site.


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.



==================


Looking into the post by @amalm, I do not see and do not understand what was the reason and the necessity to take my clear explanation 
and to re-write it in much worse style.


My method is very standard method to solve this problem.


The method from the amalm&#39;s post is non-standard, and if you come to the teacher with his solution instead of mine,

the teacher will see momentarily that you do not know the standard method and do not know standard and basic facts on logarithms.


</PRE>