Since log_3(13) = 1/(log_13(3))log3(13)=1log13(3)
we have
(log_3(13))(log_13(x))(log_x(y) ) = (log_13(x) /(log_13(3)))(log_x(y) )(log3(13))(log13(x))(logx(y))=(log13(x)log13(3))(logx(y))
The quotient with a common base of 13 follows the change of base formula, so that
log_13(x) /(log_13(3)) = log_3(x)log13(x)log13(3)=log3(x), and
the left hand side equals
(log_3(x))(log_x(y))(log3(x))(logx(y))
Since
log_3(x) = 1/(log_x(3))log3(x)=1logx(3)
the left side equals
log_x(y)/log_x(3)logx(y)logx(3)
which is a change of base for
log_3(y)log3(y)
Now that we know that log_3(y) = 2log3(y)=2, we convert to exponential form, so that
y = 3^2 = 9y=32=9.