Question 1057131
When you have something like log (base 9) 4, you can rewrite it as {{{log 4 / log 9}}}


And when you do that, you can use any base for the logarithms that you want.


So, instead of using the common base-10 log, we can write is using a base-3 log:


{{{log9 (4) = log 4 / log 9 = log3 (4) / log3 (9)}}}


But log3 (9) = 2:


{{{log9 (4) = log3 (4) / 2}}}


Substituting {{{log3(4)/2}}} in place of {{{log9(4)}}} gives:



{{{3^(log3(4)/2)}}}


which equals:


{{{sqrt(3^(log3(4)))  }}}


And since {{{3^(log3(4)) = 4 }}}, the expression is equal to:


{{{sqrt(4) = 2}}}