Question 896326
Not know what you mean.  Your expression on the left, badly formed, have no input for the logarithm function.  If your "^" mark indicates the input, then this is wrong.

A wild guess is that you want this:
{{{log((x-9))log((x))=1}}}, for Common Logs.


{{{log((x-9))=1/log((x))}}}


{{{log((x-9))=-log((x))}}}


{{{log((x-9))=log((x^(-1)))}}}-------Then these inputs must be equal.


{{{x-9=x^(-1)}}}

{{{x-9=1/x}}}
{{{x-1/x-9=0}}}-------Note that whatever found, {{{highlight_green(x<>0)}}}.
{{{x^2-1-9x=0}}}
{{{x^2-9x-1=0}}}
-
{{{x=(9+- sqrt(81+4))/2}}}
{{{highlight(x=(9+- sqrt(85))/2)}}}