\( \log _{3} 405-\log _{3} 5=\square \) (Type an exact answer in simplified form. Use integers or frac

To simplify \( \log_{3} 405 - \log_{3} 5 \), you can use the logarithm property that states \( \log_{a} b - \log_{a} c = \log_{a} \left(\frac{b}{c}\right) \). So, we have: \[ \log_{3} 405 - \log_{3} 5 = \log_{3} \left(\frac{405}{5}\right) \] Now, calculate \( \frac{405}{5} \): \[ \frac{405}{5} = 81 \] Now plug that back into the logarithm: \[ \log_{3} 81 \] Since \( 81 = 3^4 \), we can rewrite the logarithm: \[ \log_{3} 81 = \log_{3} (3^4) = 4 \] Thus, the simplified answer is: \[ \boxed{4} \]