Question 68563
<pre><font face = "lucida console">with the exponet of 5 radical sign over 125/.55 show process using logarithms (sorry index of 5)
{{{root(5,125/.55)}}} =
{{{(125/.55)^(1/5)}}} =
Now use the principle that {{{X = 10^(log(X))}}} to rewrite the above:
<font size = 3><sub>10^</sub></font>{{{log((125/.55)^(1/5))}}}
Now use the principle that {{{log(X^N) = N*log(X)}}} to rewrite 
the exponent of 10:
<font size = 3><sub>10^</sub></font>{{{(1/5)log((125/.55))}}}
Now use the principle {{{log(X/Y) = log(X)-log(Y)}}} to rewrite
the above as:

<font size = 3><sub>10^</sub></font>{{{(1/5)(log(125)-log(.55))}}}

Now use a calculator to get log(125) = 2.096910013 and
log(.55) = -.2596373105

<font size = 3><sub>10^</sub></font>{{{(1/5)(2.096910013-(-.2596373105))}}}
or
<font size = 3><sub>10^</sub></font>{{{(1/5)(2.096910013+.2596373105)}}}
or
<font size = 3><sub>10^</sub></font>{{{(1/5)(2.356547324)}}} 
or
<font size = 3><sub>10^</sub></font>{{{(.4713094647)}}}
or
2.960121005
Edwin</pre>