Please help me!!

Simply use some creative algebraic manipulation with the property of logarithms to find an approximation for the other expressions.

a) $\log_{5}2$

There are probably many approaches that would lead to the same answer, but here is how I would approach this one:

$\log_{5}8 =\log_{5}2^3 \\ \log_58 = 3\log_52 \\ 1.2920 = 3\log_52 \\ \log_52 = \frac{1.2920}{3} \approx 0.4307$

b) $\log_5 \frac{75}{8}$

Luckily, we use the result from before to help this particular problem.

$\log_5 \frac{75}{8} = \log_5 75-\log_5 8 \\ \log_5 \frac{75}{8} = \log_5 (3*25) - \log_5 8\\ \log_5 \frac{75}{8} = \log_5 3 + \log_5 25 - \log_5 8\\ \log_5 \frac{75}{8} = 0.6826 + 2 - 1.2920 \approx 1.3906 \\ $

You can check to determine if your answer is reasonable by using a calculator and evaluating $\log_5 2$ and $\log_5 \frac{75}{8}$. The decimal expansion should be match up for the first few digits.