If $\log _{b} 8=0.21$, evaluate the expression. \[ \log _{b} \frac{5}{40} \] \[ \log _{b} \frac{5}{40}= \] (Simplify your answer.)

Step 1 ：The expression \(\log _{b} \frac{5}{40}\) can be simplified as \(\log _{b} \frac{1}{8}\).

Step 2 ：Since we know that \(\log _{b} 8=0.21\), we can use the property of logarithms that \(\log _{b} \frac{1}{x} = -\log _{b} x\) to find the value of \(\log _{b} \frac{1}{8}\).

Step 3 ：\(\log_b_8 = 0.21\)

Step 4 ：\(\log_b_1_over_8 = -0.21\)

Step 5 ：Final Answer: The value of \(\log _{b} \frac{5}{40}\) is \(\boxed{-0.21}\).