If $\log _{b} 5=0.7, \log _{b} 3=0.5$, evaluate the following.
\[
\log _{b} \frac{5}{3}
\]
\[
\log _{b} \frac{5}{3}=
\]
(Simplify your answer.)

Answer

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Answer

Thus, the value of $\log _{b} \frac{5}{3}$ is approximately $\boxed{0.2}$.

Steps

Step 1 ：Given that $\log _{b} 5=0.7$ and $\log _{b} 3=0.5$, we are asked to evaluate $\log _{b} \frac{5}{3}$.

Step 2 ：Using the properties of logarithms, we know that $\log_b \frac{a}{c} = \log_b a - \log_b c$.

Step 3 ：Substituting the given values, we get $\log_b \frac{5}{3} = \log_b 5 - \log_b 3 = 0.7 - 0.5$.

Step 4 ：Solving the above expression, we get $\log_b \frac{5}{3} = 0.2$.

Step 5 ：Thus, the value of $\log _{b} \frac{5}{3}$ is approximately $\boxed{0.2}$.