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

To solve the equation $log_{3}(\frac {1}{3})+log3^{-\frac {1}{9}}x=5$, we can use the properties of logarithms.<br /><br />First, let's simplify the left side of the equation:<br /><br />$log_{3}(\frac {1}{3})$ can be simplified to $-1$, since $\frac {1}{3}$ is the reciprocal of $3$.<br /><br />Next, $log3^{-\frac {1}{9}}x$ can be simplified to $-\frac {1}{9}x$, since $log3^{-\frac {1}{9}}$ is the exponent of the base $3$.<br /><br />Now, we can rewrite the equation as:<br /><br />$-1 - \frac {1}{9}x = 5$<br /><br />To solve for $x$, we can add $1$ to both sides of the equation:<br /><br />$-\frac {1}{9}x = 6$<br /><br />Finally, we can multiply both sides of the equation by $-9$ to isolate $x$:<br /><br />$x = -54$<br /><br />Therefore, the solution to the equation is $x = -54$.