Question 145816
Express in terms of sums and differences of logarithms 
{{{log((5a/(4b^2)))}}} 
<pre><font size = 4 color = "indigo"><b>
Use this rule:----------- {{{log((X/Y))=log((X))-log((Y))}}}

{{{log((5a))-log((4b^2))}}}

Use this rule:-----------    {{{log((XY))=log((X))+log((Y))}}}
on both terms above being very careful to put the
results of the second term in parentheses because
it has a minus sign in front of it, which will 
change the signs:

{{{(log((5))+log((a)))-(log((4))+log((b^2)))}}}
 
Now remove the prentheses:

{{{log((5))+log((a))-log((4))-log((b^2))}}}

Use this rule:----------- {{{log((X^N))=N*log((X))}}}
on the last term:

{{{log((5))+log((a))-log((4))-2*log((b))}}}

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</pre></b>
Write in simplest radical form:

{{{root(3,5x^5)}}}
<pre><font size = 4 color = "indigo"><b>
Write that as

{{{root(3,5*x*x*x*x*x)}}}

The index is 3 (cube root),
we make as many groups of three like factors
as we can and leave the others ungrouped, like
this:

{{{root(3,5*(x*x*x)*x*x)}}}

We were only able to make one group in this
problem but in other problems you can make more
groups.

The TRIPLE {{{(x*x*x)}}} comes out in front as a 
SINGLE {{{x}}} and the other factors stay underneath
the radical:

{{{x*root(3,5*x*x)}}}

Then you write the {{(x*x}}} under the radical as {{{x^2}}}

{{{x*root(3,5x^2)}}}

------------------------------
Edwin</pre></font></b>