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

Answer

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Answer

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

Steps

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 $\boxed{-0.21}$.

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

Answer

Popular Problems

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