Solve for $x$ in the following equations.

1. $\log_{3} 81 = x$

   Hint (a):

   $3^{x} = 81$

2. $5^x =\frac { 1 } { 5 }$

   Hint (b):

   $5^{x} = 5^{−1}$

3. $3x = 7$

   Hint (c):

   $\log3^{x} = \log7$

4. $9^{2x}= 27^{x−2}$

   Hint (d):

   $\left(3^{2}\right)^{2x} = \left(3^{3}\right)^{x−2}$

5. $\log_{2} [\log_{9} \left(\log_{3} x\right)] = −1$

   Step 1(e):

   $2^{−1} = \log_{9}\left(\log_{3}x\right)$

   $\text{log}_{9}(\text{log}_{3}x)=\frac{1}{2}$

   Step 2(e):

   $9^{1/2}=\log_3x$

   $\text{log}_{3}x = 3$

   Step 3(e):

   $3^{3} = x$

6. $\left(x − 3\right)\left(\ln x − 2\right) = 0$

   Hint (f):

   $x − 3 = 0$
   Solve for $x$.
   
   $\ln x − 2 = 0$
   Solve for $x$.