Solving Logarithmic Equations

Solve

$$\log_3x=1$$  

(a)  

$$\log\left(9-x\right)=\log\left(2x-6\right)$$  

(a)  

$$\log_3\left(n^2+4n\right)=\log_3\left(35+2n\right)$$  

$$\log_9\left(r-8\right)\ =\ 2$$  

(a)  

$$\log_6\ \left(x\ +\ 1\right)=1$$  

(a)  

$$\log_4\ 7\ +\ \log_{4\ }\ \left(x\ -\ 2\right)\ =\ \log_4\ 62$$  

$$\log_4\ 6\ -\ \log_4\ 4x\ =\ \log_{4\ }63$$  

$$\log_7\ \left(x\ +\ 4\right)\ -\ \log_{7\ }x\ =\ \log_{7\ }33$$  

$$\log_9\left(r-8\right)\ =\ 2$$  

(a)  

Solve for x.
$$\log_{20}\left(2x-100\right)=3$$