Question 896431
That seems to be asking for this:
{{{highlight_green(log(b,512)=6)}}}, and you want to find b.


{{{512=2^9}}}; so you have
{{{log(b,2^9)=6}}}
-
{{{3*log(b,2)=2}}}
{{{log(b,2)=2/3}}}


{{{b^(2/3)=2}}}


{{{(b^(2/3))^(3/2)=2^(3/2)}}}


{{{highlight(b=2^(3/2))}}}
which you could convert into {{{sqrt(2)sqrt(2)sqrt(2)}}}
{{{highlight(highlight(2sqrt(2)))}}}.