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 $0.2$ .

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 $0.2$ .