Find x if log_(3)((1)/(3))+log3^((1)/(9))=5

To solve the equation $log_{3}(\frac {1}{3})+log3^{(\frac {1}{9})}=5$, we can use the properties of logarithms.<br /><br />First, let's simplify the left side of the equation:<br /><br />$log_{3}(\frac {1}{3})+log3^{(\frac {1}{9})}$<br /><br />We can rewrite $\frac {1}{3}$ as $3^{-1}$ and $\frac {1}{9}$ as $3^{-2}$:<br /><br />$log_{3}(3^{-1})+log3^{(3^{-2})}$<br /><br />Using the property of logarithms that states $log_{b}(b^{x}) = x$, we can simplify further:<br /><br />$-1 + (-2)$<br /><br />This simplifies to:<br /><br />$-3$<br /><br />So, the equation becomes:<br /><br />$-3 = 5$<br /><br />This equation is not possible, as -3 is not equal to 5. Therefore, there is no solution for x that satisfies the given equation.