Question 606063
Let <img src="http://latex.codecogs.com/gif.latex?\LARGE x = \log_{\frac{1}{3}}\left(9\right)" title="x" />

Convert this equation to exponential form to get {{{(1/3)^x=9}}}. Now let's solve for x

{{{(1/3)^x=9}}}

{{{(3^(-1))^x=3^2}}}

{{{3^(-1*x)=3^2}}}

{{{3^(-x)=3^2}}}

Since the bases are equal (to 3), the exponents must be equal. So {{{-x=2}}} or {{{x=-2}}}

So the solution is {{{x=-2}}}

Since we let <img src="http://latex.codecogs.com/gif.latex?\LARGE x = \log_{\frac{1}{3}}\left(9\right)" title="x" /> at the top of the problem, we can say that

<img src="http://latex.codecogs.com/gif.latex?\LARGE \text{\color{red}Answer:} \ \color{blue}\boxed{\log_{\frac{1}{3}}\left(9\right) = \color{red} -2}" title="x" />

Note: you can use the change of base formula to get the same answer of -2.

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