Question 98950
how do you to the log base 2 of the third root of 32.
if you could explain too
<pre><font size = 3><b>

               log<sub>2</sub>{{{root(3,32)}}}

Rewrite {{{root(3,32)}}} as {{{32^(1/3)}}}

               log<sub>2</sub>{{{32^(1/3)}}}

Break 32 into prime factors:  32 = 2򈭾򈭾 = {{{2^5}}}
then replace 32 by {{{2^5}}}

               log<sub>2</sub>{{{(2^5)^(1/3)}}}

Remove the parentheses by multiplying the inner exponent 5
by the outer exponent {{{1/3}}} to get {{{5/3}}}

               log<sub>2</sub>{{{2^(5/3)}}}

Use the principle log<sub>b</sub>{{{b^n)}}} = {{{n}}}

               {{{5/3}}}

That's the answer. 

Edwin</pre>