Answer
{$\frac{43}{21}$}
Work Step by Step
Step 1: $\log_{4} (x+1)-\log_{4} (x-2)=3$
Step 2: $\log_{4} (\frac{x+1}{x-2})=3$
Step 3: $(\frac{x+1}{x-2})=4^{3}$
Step 4: $(\frac{x+1}{x-2})=64$
Step 5: $x+1=64(x-2)$
Step 6: $x+1=64x-128$
Step 7: $64x-128=x+1$
Step 8: $64x-x=1+128$
Step 9: $63x=129$
Step 10: $x=\frac{129}{63}=\frac{43}{21}$
Step 11: Therefore, the solution set is {$\frac{43}{21}$}.
