so my advanced functions teacher didn't really explain this lesson well and i can't seem to figure it out on my own.
if you could be kind enough to explain the process i would greatly appreciate it!
The logarithm of a number y with respect to a base b is the exponent to which we have to raise b to obtain y.
the definition would be:
$\displaystyle x = log_{b} y \Longleftrightarrow b^x = y$
and we say that x is the logarithm of y with base b if and only if b to the power x equals y.
For example:
$\displaystyle 10^2 = 100 \Longleftrightarrow log_{10} 100 = 2$
and, $\displaystyle 10^{-2} = 0.01 \Longleftrightarrow log_{10} 0.01 = -2$
Based on this, can you now complete your question?!
$\displaystyle \displaystyle\ \log_9\left(\frac{1}{3}\right)=x$
$\displaystyle \displaystyle\ \log_3\left(\frac{1}{9}\right)=y$
Imagine a "fog" surrounding the "log" and the base slides over to the other side,
so we get
$\displaystyle \displaystyle\frac{1}{3}=9^x$
$\displaystyle \displaystyle\frac{1}{9}=3^y$
Now x and y will be easier to derive.