Question 846344
Log using base 81?   Review the Change of Base formula(just in case), and use conventional notation.


{{{highlight_green(log(81,5)+log(81,2x-1)=1/4)}}}.
You might think that change of base be necessary, but....

How far can this be solved WITHOUT changing bases?
Condensing the log expression, the left member,


{{{log(81,5*(2x-1))=1/4}}}


{{{81^(1/4)=5(2x-1)}}}


{{{(3^4)^(1/4)=10x-5}}}


{{{3=10x-5}}}
{{{10x=3+5}}}
{{{10x=8}}}
{{{highlight(x=4/5)}}}