Question 1090060
<pre>
{{{log(125,(1/5))}}}{{{""=""}}}{{{x}}}

ANY logarithmic equation log<sub>B</sub>(A) = C
is equivalent to the exponential equation A = B<sup>C</sup>.

Therefore your logarithmic equation is equivalent to
the exponential equation 

{{{1/5}}}{{{""=""}}}{{{125^x}}}

Next we write 1/5 as 5<sup>-1</sup> and 125 as (5<sup>3</sup>)

{{{5^(-1)}}}{{{""=""}}}{{{(5^3)^x}}}

We multiply the exponents on the right to remove the
parentheses:

{{{5^(-1)}}}{{{""=""}}}{{{5^(3x)}}}

Now Since the bases of the exponents on the laft and right are
equal, positive, and different from 1, the exponents must also
be equal, so we can drop the bases and set the exponents equal:

{{{-1}}}{{{""=""}}}{{{3x}}}

Divide both sides by 3

{{{-1/3}}}{{{""=""}}}{{{x}}}

Edwin</pre>