Answer
d) 2.0574
e) 0.2878
Step-by-step explanation
Change of base formula
[tex]\log_ab=\frac{\log_cb}{\log_ca}_[/tex]
d) Applying this formula to this case and using a base of 10 in the new logarithms, we get:
[tex]\begin{gathered} \log_{20}475=\frac{\log_{10}475}{\log_{10}20} \\ \log_{20}475=\frac{2.6767}{1.3010} \\ \log_{20}475=2.0574 \end{gathered}[/tex]
e) Applying this formula to this case and using a base of 10 in the new logarithms, we get:
[tex]\begin{gathered} \log_{15}2.18=\frac{\log_{10}2.18}{\log_{10}15} \\ \log_{15}2.18=\frac{0.3385}{1.1761} \\ \log_{15}2.18=0.2878 \end{gathered}[/tex]
