Question 953289

    Log Rules:

    1) {{{log(b,(mn)) = log(b,(m)) + log(b,(n))}}}

    2) {{{log(b,(m/n)) = log(b,(m)) – log(b,(n))}}}

    3) {{{log(b,(m^n)) = highlight(n *log(b,(m)))}}}...you need to apply this rule




{{{(2log(2,x))/2}}}

{{{(cross(2)log(2,x))/cross(2)}}}

{{{highlight(log(2,x))}}}..simplified using base {{{2}}}

now you can change the base if you will:

In order to evaluate a non-standard-base log, you have to use the Change-of-Base formula:

{{{log(b,(x))=log(d,(x))/log(d,(b))}}}

usually we use base {{{d=10}}}

so, you will have

{{{log(x)/log(2)}}}


your teacher shows this simplifying to {{{log(2,x^2)}}} which is wrong 

{{{2log(2,x)}}} is equal {{{log(2,x^2)}}} (using the rule from above, but given
 is {{{2log(2,x)/2}}}=>is equal to {{{log(2,x^2)/2}}} not only {{{log(2,x^2)}}}