Question 744476
<pre>
1. Show that log(base 1/c)x = log(base c)1/x

Can you please help me out? Thanks so much in advance:)
Can you please show all the steps it would really help me understand:)

      {{{log (1/c, (x)) = log (c, (1/x))}}}
      Focusing on the left side only, we get:
      {{{log ((x))/log ((1/c)) = log (c, (1/x))}}}
    {{{log (c, (x))/log (c, (1/c))}}} = {{{log (c, (1/x))}}}  ----- Changing to base c on left side
     {{{log (c, (x))/(- 1)}}} = {{{log (c, (1/x))}}}  ----- Changing {{{log (c, (1/c))}}} to - 1, as {{{c^(- 1) = 1/c}}}
   {{{- log (c, (x))}}} = {{{log (c, (1/x))}}}
{{{log (c, (x^(- 1)))}}} = {{{log (c, (1/x))}}}
  {{{highlight(highlight(log (c, (1/x))))}}} = {{{highlight(highlight(log (c, (1/x))))}}} <==== PROVEN</pre>